In a stockpot, melt 1 Tbsp of the butter over medium heat. Once melted, add the diced onions and saute until soft and fragrant, about 4-5 minutes, stirring frequently. Add the minced garlic and stir to cook about 1 minute.
Add the remaining 4 Tbsp butter and the cream cheese to the pot. Stir until it's all melted and thickened, 1-2 minutes.
Add the broth and cream to the pot and stir to combine. Reduce heat to medium-low and let simmer for about 10-15 minutes, stirring occasionally as it thickens.
Add the broccoli, carrots, salt, pepper, paprika, ground mustard and chipotle pepper powder. Stir to combine everything and continue to simmer an additional 20 minutes.
Remove the soup from the burner. Add almost all of the shredded cheddar to the pot (reserving some for topping later) and stir to combine. Let it sit for a minute or two to let the cheese melt then stir it again.
Ladle the soup into individual serving bowls and garnish with extra shredded cheese. Leftovers can be stored in the fridge in an airtight container for up to 1 week.