Chef John's Hot Sloppy Joe Dip

Name: Chef John's Hot Sloppy Joe Dip
Prep time: 15 min
Cook time: 1 h 5 min
Total time: 1 h 20 min
Yield: 12
Ingredients: 2 lbs Ground beef, lean; 4 cloves Garlic; 2 Green bell peppers; 1 Onion; 2 cups Chicken broth; 1 tbsp Dijon mustard; 1 cup Ketchup; 1 tsp Worcestershire sauce; 3 tbsp All-purpose flour; 1 tsp Black pepper, ground; 2 tbsp Brown sugar; 1 Cayenne pepper; 2 tsp Kosher salt; 1 cup Cheddar cheese