Brown the garlic in the olive oil until it is golden brown. Add the chopped beef and continue to brown. When meat is done (not too much red anymore) and well separated, add the onions and carrots and continue to cook for 2 to 3 minutes. Add the white wine and tomato paste and lower the heat to simmer. Cover and cook for 1 1/2 hours or until it appears sauce-like, adding water as needed. Season to taste with salt and pepper. Toss with cooked ziti and serve immediately.