Steam broccoli until soft. Mash about half the broccoli with a fork, set aside.
In a medium pot, heat up the oil on medium heat. Add chopped onion and shredded carrot. Saute until the onion is transparent.
Add minced garlic clove, stir well and saute until fragrant.
Sprinkle with flour and mix until veggies are coated with flour.
Slowly pour in the milk and veggie stock while constantly stirring.
Let the soup heat through (still on medium heat.) Once it starts to boil, start adding cheese.
Grate the cheddar and Swiss cheese into the pot. Stir slowly until melted. (I recommend using block cheese and grate it in yourself because it will melt much better. Pre-shredded cheese is coated in cornstarch while packaged, so it's a little harder to melt.)
Chop the Velveeta into 1-inch cubes, for faster melting, and add it to the pot. Stir slowly and constantly until the cheese is melted.
Stir in chopped bacon.
Add salt and cracked peppercorns to taste. (Since Velveeta, bacon and other cheeses have salt in it, don't add salt until you add those ingredients.)
Stir in the broccoli. Lower the heat to medium low, cover and cook for about 7-10 minutes, stirring occasionally.