Learn Icelandic: Mér þykir maturinn bragðgóður.

The verb þykja is a quirky verb. It requires the person who holds the opinion (the experiencer) to be in the dative case. So instead of ég (I), you must use mér (to me).

If the sentence means 'I find', why is the verb þykir in the third-person singular?

Because mér is in the dative case, it cannot control the verb form. The verb instead agrees with what you are having an opinion about. Here, that is maturinn (the food), which is a third-person singular noun in the nominative case, so the verb becomes þykir.

Why is bragðgóður in the nominative case here? Doesn't the verb take an object?

With þykja, the thing being evaluated is not a direct object; it stays in the nominative case. Because maturinn is nominative, masculine, and singular, the adjective describing it (bragðgóður) must match it exactly.

How is mér þykir different from mér finnst?

They are very similar and both take a dative subject to express an opinion. Mér finnst is the most common way to say 'I think' or 'I find' for general opinions. Mér þykir is often used for more deeply held personal feelings, affections, or values, though they are practically interchangeable when praising a good meal!