Place 3 tablespoons of olive oil into a saucepan over medium heat, and cook the garlic in the oil for 1 minute. Stir in the onions, and cook until translucent, about 5 more minutes. Stir in the green bell pepper, and cook until the pepper begins to become tender, about 5 more minutes. Set the vegetables aside.
Place 2 tablespoons of olive oil into a large saucepan over medium heat, and cook and stir the ground beef until the meat is no longer pink, about 10 minutes. Break the meat up into crumbles as it cooks. Mix in the mushrooms, spaghetti sauce, tomato sauce, tomato paste (if you prefer a thicker sauce), and vegetables. Bring the sauce to a boil, and reduce heat to a simmer. Cook, stirring occasionally, until the flavors have blended, about 30 minutes.
Mix the coffee granules into the hot water, and pour into the sauce; simmer for 30 more minutes.