Add the bacon to a large, heavy-bottomed pot or Dutch oven over medium heat. Cook until crispy, about 5 minutes, then transfer to a paper towel-lined plate to drain. Carefully pour the bacon fat in the pot into a small bowl or jar for later use.
Place the same pot back over medium heat, adding back 2 tablespoons of the reserved bacon fat and the diced onion. Season with the Kosher salt, then stir to combine. Cook, stirring occasionally, until the onion is softened, about 3-5 minutes. Add in the minced garlic, Dijon mustard, & paprika and cook, stirring constantly, just until the garlic is fragrant, about 30 seconds. Sprinkle in the all-purpose flour and stir to combine. Cook another 1-2 minutes, until the flour is dark in color - that’s where the flavor comes from!
Slowly pour the beer into the soup pot, using a wooden spoon to scrape any brown bits off the bottom of the pot. Allow the beer to reduce down for 1 minute, then pour in the chicken stock and heavy cream. Bring the mixture to a boil, then reduce to a simmer. Simmer for 5 minutes, until the soup is slightly thickened.
Add in the broccoli and carrots, cooking until the broccoli is bright green and tender, about 5 minutes. If desired, use an immersion blender to blend the soup to your desired consistency. Completely blending the soup will yield a super thick & creamy soup; forgoing blending will make the soup soup-ier. Gently stir in the cheese, until it melts and thickens the soup.
Serve immediately, topped with reserved bacon & extra shredded cheese, and alongside some buttered crusty bread. Enjoy!
