1. Heat soffritto base in a large pot over medium-high heat. Add peppers and cook, stirring to coat. Continue cooking until peppers are softened, about 3 minutes. Add potatoes and stir to combine.

2. Add bay leaves and enough water to cover the vegetable mixture by about 1 inch (about 9 cups); season with salt and pepper and bring to a boil. Reduce heat to a simmer and cook until pepper and potatoes are almost soft, about 30 minutes.

3. Crush the thyme with the flat side of a knife and add it to the pot. Continue to simmer until peppers and potatoes are completely soft, about 15 minutes more.

4. Remove bay leaves and thyme; discard. Working in batches, pass soup through a food mill fitted with a fine disk. Whisk in 1/2 cup olive oil, if desired; season with salt and pepper. If soup seems too thick, add a little water to thin out. Serve warm, drizzled with olive oil and garnished with croutons and thyme leaves.