Dice bacon into 1/4-inch cubes.
Place in a heavy 6-quart pot over medium-low heat.
Cook until fat is rendered and translucent.
Add onion, carrot, celery and garlic.
Cook until onion and garlic are soft and translucent; season with salt and pepper.
Add split peas, stir to coat with fat, and add bay leaves and 2 quarts stock.
Increase heat and bring to a boil.
Reduce heat so soup simmers.
Skim foam that rises to the surface for about 10 minutes, until no more appears.
Add thyme leaves.
Simmer, uncovered, about 1 hour or longer, until peas are soft and starting to fall apart.
Add more stock, as needed.
Remove soup from heat.
Add salt and pepper, to taste.
Purée soup with an immersion blender, right in the pot, or pour into a food processor, in several batches, short of perfect smoothness; you should be able to spoon up some texture.
Reheat soup, skimming off any foam.
Stir from the bottom to mix well, then ladle into bowls and serve.
