À mon avis, les poireaux et le brocoli donnent meilleur goût à la soupe que les petits pois.

À mon avis means in my opinion.

Literally, à here is part of a fixed expression. French often uses à in set phrases like this:

• à mon avis = in my opinion
• à mon sens = in my view
• selon moi = according to me / in my opinion

So you should learn à mon avis as a whole expression rather than trying to translate each word separately.

French usually uses definite articles much more often than English when talking about things in a general sense.

So:

• les poireaux = leeks, in general
• le brocoli = broccoli, in general
• les petits pois = peas, in general

English often drops the article in these cases, but French normally keeps it.

That is why les poireaux et le brocoli sounds natural in French, even though English would usually just say leeks and broccoli.

Poireau is a singular noun meaning leek.

Its plural is poireaux. This is a common plural pattern for some French nouns ending in -eau:

• un poireau → des poireaux
• un bateau → des bateaux
• un château → des châteaux

So the -x is just the normal plural ending for this type of word.

The subject is les poireaux et le brocoli.

Even though le brocoli is singular, the whole subject has two parts joined by et:

• les poireaux
• le brocoli

Together, that makes a plural subject, so the verb must also be plural:

• les poireaux et le brocoli donnent

If it were only one thing, you would use singular:

• Le brocoli donne meilleur goût à la soupe.

Because meilleur agrees with goût, not with soupe.

In meilleur goût:

• goût is a masculine singular noun
• so the adjective is meilleur

Compare:

• un meilleur goût → masculine singular
• une meilleure saveur → feminine singular
• de meilleurs résultats → masculine plural
• de meilleures idées → feminine plural

Even though soupe is feminine, meilleur is not describing the soup directly here. It is describing the goût.

In this sentence, donner goût à quelque chose works a bit like an expression, and French often omits the article in this kind of structure.

So donner meilleur goût à la soupe means to give the soup a better taste or to make the soup taste better.

You may also hear or see slightly different versions depending on style, such as:

• donner un meilleur goût à la soupe
• donner meilleur goût à la soupe

Both are understandable, but the version without un is very natural in this kind of general statement.

Because the structure is donner quelque chose à quelque chose in the sense of to give something to something.

Here:

• donner meilleur goût à la soupe = to give a better taste to the soup

French treats la soupe as the thing receiving the improved taste, so à is used.

If you said dans la soupe, that would mean in the soup, which focuses more on physical location, not on the idea of giving flavor to it.

So:

• à la soupe = to the soup
• dans la soupe = in the soup

It compares what kind of taste the different vegetables give to the soup.

The structure is:

• X donnent meilleur goût à la soupe que Y

This means:

• X give the soup a better taste than Y do

So here the comparison is between:

• les poireaux et le brocoli and
• les petits pois

In fuller English, the idea is:

• Leeks and broccoli give the soup a better taste than peas do.

French often leaves out the repeated verb because it is understood.

Les petits pois is the normal French term for peas or more specifically green peas.

It is plural because peas are usually thought of as multiple small items:

• un petit pois = a pea
• les petits pois = peas

The adjective petits is part of the standard expression. French does not usually just say les pois when referring to ordinary green peas in this everyday food sense. Petits pois is the usual phrase learners should remember.

Not with the same meaning.

• ont meilleur goût means taste better or have a better taste
• donnent meilleur goût à la soupe means give the soup a better taste

So these are different ideas:

• Les poireaux et le brocoli ont meilleur goût que les petits pois.
  = Leeks and broccoli taste better than peas.

• Les poireaux et le brocoli donnent meilleur goût à la soupe que les petits pois.
  = Leeks and broccoli make the soup taste better than peas do.

The original sentence is about what improves the soup, not about which vegetable tastes better on its own.

Yes. A few natural alternatives are possible, for example:

• À mon avis, les poireaux et le brocoli donnent à la soupe un meilleur goût que les petits pois.
• À mon avis, la soupe a meilleur goût avec des poireaux et du brocoli qu’avec des petits pois.
• À mon avis, les poireaux et le brocoli rendent la soupe meilleure que les petits pois.

These all express a similar idea, but the original sentence is perfectly natural. It emphasizes that leeks and broccoli give the soup a better flavor than peas do.