Heat a large nonstick skillet over medium heat and spray with nonstick cooking spray.
Add the ground beef and cook, stirring frequently, until browned, about 5 minutes; break up any large pieces.
Stir in the chopped onion and garlic and cook until softened, about 5 minutes.
Add the chopped carrot and cook about 2 minutes, then stir in the chopped mushrooms and cook briefly to combine.
Add the canned diced tomatoes, tomato paste, dried basil, and dried oregano; bring the mixture to a boil.
Reduce heat to low, cover, and simmer for 10 minutes.
Uncover, stir in the skim milk, and continue cooking uncovered until the sauce thickens, about 15 minutes; season with salt and pepper to taste.
Meanwhile, cook the whole wheat spaghetti according to package directions and drain.
Divide the cooked spaghetti among 4 bowls, spoon the bolognese sauce over each serving, and garnish with fresh basil if desired.