Pour off juice from carrots and smash the carrots with a potato masher.
In a dutch oven on medium high, add garlic, minced onion, and butter. Saute until butter is completely melted.
Add flour and stir constantly to prevent lumps. Make sure to keep stirring until it’s completely combined with the butter. It will thicken and bubble. This makes a roux (like for gravy, etc.)
Keep stirring and just as it starts to turn brown, turn the fire down to medium and add chicken broth, carrots, broccoli, 2 cups of water, salt, and garlic powder.
Keep stirring until all the ingredients are well combined.
Allow to cook for 30 minutes, stirring every few minutes, until the broccoli is tender.
Add 2 additional cups of water and Velveeta shells and cheese and stir.
Add Velveeta shredded cheese 1 cup at a time while stirring to allow it to melt.
Once all ingredients are added, stir occasionally and let cook for another 10 minutes.
