This question was already asked a couple of times, here and here for example, although no answer was accepted.

Both des and les can be used in your sentences.

Comment xxxx des légumes ?

means

How to xxxx vegetables ? (any kind of them)

while

Comment xxxx les légumes ?

means

How to xxxx the vegetables ?

with xxxx being one of the verbs of your examples (confire, braiser, cuisiner, blanchir, préparer…).

Here the meaning might be identical to the previous form, when the vegetables is representing “the vegetables in general” but it might also means “the vegetables that we are talking about, the vegetables I need to cook”. The context should help figuring out which meaning is intended.

In the last sentence:

Je prépare des légumes frais pour cette salade

You tell you are using some fresh vegetables to make this salad while in:

Je prépare les légumes frais pour cette salade

you tell you use the fresh vegetables (all the ones that are already here) to make the salad.

“Je mange des légumes.” means : I eat vegetables. You don’t know which are the vegetables. It is “indéfini“.

“Je mange les légumes” would be equivalent to : I eat the vegetables. You know that you eat these vegetables. It is “défini“.

Example : Je mange des légumes tous les jours. Mais aujourd’hui, j’ai mangé les légumes du jardin.