Start by dicing the onion, chopping the celery, and slicing the carrots thinly. Mince the garlic cloves and set all aside.
Pour a tablespoon of olive oil into the crockpot and add the diced onion, celery, and sliced carrots. Cover and cook on low for about 2 hours until the vegetables are fragrant and slightly softened, or just toss everything raw if you're short on time.
Add the minced garlic and canned tomatoes (with juices) into the crockpot. Stir to combine everything evenly, releasing a fragrant aroma as the garlic cooks.
Pour in the vegetable broth and season with dried thyme, basil, salt, and pepper. Stir well to distribute the herbs and seasoning.
Close the lid and set the crockpot to low for 6-8 hours, or on high for about 4 hours. The house will fill with a savory, bubbling aroma as the flavors meld and the vegetables become tender.
About 20 minutes before serving, add the small pasta shapes to the crockpot. If the soup is too thick, pour in a bit more broth to loosen it up. Cover and cook on high until the pasta is tender, approximately 15-20 minutes.
Once the pasta is cooked through, taste and adjust the seasoning with more salt or pepper if needed. Squeeze in some fresh lemon juice for brightness and stir in chopped fresh herbs if available.
Serve the minestrone hot in bowls, topped with grated Parmesan or cheese if desired, and a drizzle of good olive oil. Enjoy the comforting, fragrant, vegetable-rich broth with tender beans and pasta.