Heat butter in a large saucepan over medium-high heat. Once melted, add the onion and carrot and saute until golden, about 7 minutes. Add the garlic, oregano, and red pepper flakes and cook 1 more minute. Add the tomatoes with their juice, bay leaf, sugar, and 2 teaspoons salt and bring to simmer. Reduce heat to medium-low and continue to cook, stirring occasionally, about 30 more minutes.
Prepare pasta while sauce simmers. Bring a large pot of generously salted water to a boil. Add the pasta and cook according to the package directions until al dente, about 12 minutes. Drain.
Remove sauce from heat, remove bay leaf, and carefully blend, in batches, to break up large pieces. Mix sauce with pasta. Serve individual portions topped with a heaping tablespoon of ricotta and garnish with basil.
Cut each link evenly in half lengthwise. Heat a grill pan over medium-high heat until hot. Place the sausage cut side down and cook, turning on all sides for even browning, until cooked through, about 10 minutes. Serve as an accompaniment with the bucatini marinara.