Bring a pot of salted water to a boil and cook the whole wheat spaghetti according to package directions; drain and keep warm.
Heat a large nonstick skillet over medium heat and lightly spray with nonstick cooking spray.
Add the lean ground beef and cook, stirring frequently, until browned, about 5 minutes; break up any large pieces.
Add the finely chopped onion and garlic to the pan and cook, stirring occasionally, until softened, about 5 minutes.
Stir in the chopped carrot and cook for about 2 minutes.
Add the chopped mushrooms, canned diced tomatoes, and tomato paste, then sprinkle in the dried basil and 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 to cook uncovered until the sauce thickens, about 15 minutes; season with salt and pepper to taste.
Divide the cooked spaghetti among four bowls, top with the bolognese sauce, and garnish with fresh basil if desired.