Have a 4-6 quart slow cooker ready to go.
Heat the oil or butter in a large skillet. Add the onion, carrot, and celery. Cook, stirring often, until the vegetables start to soften.
Add the garlic and cook for 30-60 seconds.
Next add the ground beef, using a wooden spoon to break it up as it cooks.
Once it has browned, remove from heat and transfer everything to the slow cooker.
Stir in the tomato paste, diced tomatoes, and ½ teaspoon salt.
Set slow cooker to HIGH for 3-4 hours, or LOW for 8-10 hours.
Before serving, taste and add more salt if needed, and season with black pepper.
Serve over hot, cooked pasta and garnish with cheese.
