In a large frypan warm olive oil over low heat; saute onion, garlic and celery until onion is transparent.
Stir in butter and increase heat to medium; brown beef until no longer pink. Mix in sugar, 1 teaspoon salt, mint and mushrooms; lower heat and stir for about 3 minutes.
In a large bowl, combine tomato paste and broth; pour liquid and basil to pot. Simmer over very low heat for about 2 hours, stirring occasionally.
Bring a large pot of water to a vigorous boil with 3 tablespoons salt and 1 teaspoon olive oil. Slip spaghetti into water holding on to ends until strands soften a bit. Cook over high heat for 7 to 8 minutes only. When properly cooked, raw taste should be gone but still have a firm texture.