Learn Finnish: Keitän porkkanoita ja perunoita.

Both base words end in -a and have three syllables. When forming the partitive plural for words like this (especially those ending in -na, -la, or -ra), the final -a changes to an -o- before adding the plural -i-. Then we add the partitive ending -ta.

Why are the partitive endings here -ta instead of just -a?

In the plural partitive, you must use the -ta (or -tä) ending if the stem ends in a diphthong (two vowels pronounced together). Because the -o- and the plural -i- combine to form the diphthong -oi- in both porkkanoita and perunoita, the required ending is -ta.

Why are the carrots and potatoes in the partitive case to begin with?

Using the partitive plural shows an unspecified quantity—you are boiling "some" carrots and potatoes. If you used the plural nominative for the total object (Keitän porkkanat ja perunat), it would mean you are boiling a specific, known batch of vegetables completely (I will boil the carrots and potatoes).

Can I use keittää to mean "to cook" in a general sense?