Sauté the vegetables
Heat olive oil or butter in a large pot over medium heat. Add the onion, carrots, and celery and cook for 5–7 minutes, until softened. Stir in the garlic and cook for about 30 seconds.
Add the rinsed split peas, thyme, bay leaf, chicken broth, and a generous pinch of black pepper. Bring to a gentle boil.
Simmer.
Reduce heat to low, cover, and let simmer for 60–75 minutes, stirring occasionally, until the split peas are very soft and starting to break down.
Add the ham. Stir in the diced ham and continue to simmer for another 10–15 minutes, until heated through.
Remove the bay leaf. Taste and season with salt as needed (go light at first — the ham adds salt).
For a creamier texture, use an immersion blender for a few quick pulses or gently mash with a spoon.