I heat up a couple T if olive oil and sauté a handful of chopped carrot, a medium chopped onion, & a handful of chopped celery if I have it. When they’ve been going for a few minutes I add a healthy pour of dry white wine and let that go for five minutes or so.
While that’s going I pick over and rinse a bag and of split peas. Those go into the pot, get all stirred up in the veggie goodness, then I add water or (homemade) stock and bring it up to a simmer. Add a bay leaf and some thyme sprigs if I have them, and put the lid on for an hour or so.
If you like ham (we do!) I usually buy a big smoked pork shank and simmer it for a few hours before I make the soup. This way I don’t have to worry about fishing weird blobs of fat etc out and can just pick over the meat while the soup cooks. Nothing wrong with putting the whole thing in the pot, either. I add the meat when the peas are starting to fall apart. Two hours maybe? Season to taste, fish out the bay leaf etc.