Heat oil in a Dutch oven over medium heat. Add onion, carrot and celery and cook, stirring, until just tender, 5 to 7 minutes. Add sliced garlic, thyme and crushed red pepper and cook, stirring, until fragrant, about 15 seconds.
Increase heat to high and add broth, tomatoes and their juice. Bring to a boil, scraping up any browned bits. Stir in collard greens (or kale), reduce heat to maintain a simmer and cook, stirring occasionally, until the greens are tender, 5 to 10 minutes. Discard the thyme sprig. Stir in black-eyed peas; remove from the heat and cover.
Position rack in upper third of oven; preheat broiler.
Place baguette slices on a baking sheet and broil until lightly toasted, 2 to 4 minutes. Rub each bread slice with the remaining garlic clove. (Discard garlic.) Turn the slices over and top with cheese. Broil until the cheese is melted, 1 to 3 minutes. Serve the soup topped with the cheese toasts.