Cook the broccoli. Add water to a pot and bring to a boil. Add broccoli to boiling water and cover. Cook for 5 to 6 minutes, or until just tender. Drain and run cold water over broccoli for 1 minute or until cooled.
Blend. In a blender, combine the cooked broccoli, cream cheese, mayo, milk, 1/2 cup shredded cheeses, garlic cloves, salt, and pepper. Process until well blended and smooth.
Bake. Transfer mixture to a 1-quart baking dish and sprinkle with remaining cheese. Bake for 25 minutes or until hot and bubbly.
Serve. Remove from oven and let stand about 5 minutes. Serve the cheese dip with veggies for dipping.