Melt butter with olive oil in a small skillet over medium-high heat. Cook and stir mushrooms in butter mixture until softened, 2 to 3 minutes. Add 1/4 cup red wine; bring to a simmer, reduce heat to medium-low, and cook until the mushrooms are very dark and shrunken in size, about 20 minutes.
Heat a large pot over medium heat. Cook and stir ground beef, yellow onion, diced tomatoes, red bell pepper, green bell pepper, and garlic together until the beef is completely browned, about 10 minutes; season with oregano, basil, and rosemary. Stir 3/4 cup red wine and tomato paste into the beef mixture. Pour spaghetti sauce into the pot; stir. Return mixture to a simmer and continue cooking until the flavors blend, 10 to 30 minutes.
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