Heat olive oil in a large skillet over medium heat. Add onion, carrot, and garlic, and sauté until aromatic and translucent, about 5 minutes. Add thyme, rosemary, and red pepper flakes. Season with salt and pepper. Sauté for an additional 3 minutes. Scrape mixture into slow-cooker insert. Alternatively, you can skip this step and add all ingredients (including the oil) into the slow cooker—you won't get as much depth of flavor, but ultimately it will all be fine and taste great.
Dump tomatoes into a medium bowl, then use your hands to break them into uneven pieces. Add to the slow cooker. Stir beans, stock, bay leaf, and Parmesan rind into the slow cooker. Season with more salt and pepper. Place lid on slow cooker and cook on high for 3 hours, or on low for 5 hours.
Remove Parm rind and season with more salt and pepper. If you’re not planning to finish all the soup tonight, cook the pasta separately in a medium pot of salted water according to the package directions until just al dente, even a little under. Scoop 1/4 to 1/2 cup cooked pasta into each serving bowl, then ladle the soup over. (Store leftover pasta separately from leftover soup—this prevents the pasta from turning into mush as you eat leftovers.) If planning to finish all the soup tonight, stir dry pasta directly into the soup, then cook for another 15 minutes.
Rebecca Firkser is a freelance food writer and recipe developer. Her work has appeared in a number of publications, among them Food52, TASTE, Edible Manhattan, Extra Crispy, The Strategist, and Bon Appetit's Healthyish. She contributed recipes and words to the book "Breakfast: The Most Important Book About the Best Meal of the Day." Once upon a time, she studied theatre design and art history at Smith College, so if you need a last-minute avocado costume or want to talk about Wayne Thiebaud's cakes, she's your girl.