In skillet, melt butter over medium heat. Add in onion and saute until translucent and softened. Sprinkle in flour and toss onions and garlic to coat. Add into slow cooker.
Pour chicken stock, and half and half over the onions and garlic. Whisk to combine. Add in salt and pepper to taste.
Add in chopped broccoli, carrots, and cubed Velveeta and shredded cheese..
Turn cooker onto low for 4 hours, or high for 2 hours. Stir occasionally and cheese will melt. Serve hot.
