Warm up a large dutch oven or stock pot over medium heat for a few minutes, then add the olive oil. After a minute, add the onion and sauté, stirring often, for 4 to 5 minutes, until the onions are soft and fragrant. If the pot starts to look dry, add a splash of water.
Reduce the heat to medium-low and add the garlic, flour, salt, pepper, paprika and mustard to the pot. Stir well and let the flour cook for 1 to 2 minutes. Bring the heat up to medium-high and add the stock a half cup at a time, stirring with a whisk between additions. Once all the stock has been added, bring up the heat so the mixture comes to a low boil. Cook for an additional 7 to 10 minutes. It will thicken as it cooks.
Add the broccoli florets and chopped carrots to the pot and stir, reserving the shredded carrots. Cover and let the soup simmer for 15 minutes, until the carrots are fork-tender
Add the milk and cheese and let the soup simmer for another minute, until the cheese has completely melted. Taste and add more salt, pepper or cayenne for a kick if desired!
Divide the soup between three meal prep containers. Top with the remaining shredded cheese for garnish. Let them cool for a bit before covering and storing in the fridge.
Storage, reheating and serving notes: This soup can last for up to five days in the fridge. It’s not freezer friendly. Reheat this soup in the microwave or on the stove partially covered. I highly recommend enjoying it with your favorite crusty bread!