Position rack in upper third of oven; preheat broiler. Cook ground beef and onion in a large broiler-safe skillet over medium heat, breaking the beef into bite-size pieces with a wooden spoon, until the beef is no longer pink, about 10 minutes. Add broccoli; cook, stirring occasionally, until the broccoli is tender-crisp, about 3 minutes. Add flour, sage and garlic; cook, stirring constantly, until the beef and vegetables are well coated in the flour mixture, about 1 minute.
Add milk and bring to a simmer over medium-high heat. Cook, stirring occasionally, until thickened, 1 to 2 minutes. Stir in cream cheese and Cheddar until melted, about 1 minute. Remove from heat and stir in salt and pepper.
Mix breadcrumbs, oil and paprika in a small bowl. Sprinkle evenly over the mixture in the skillet.
Broil the casserole until the breadcrumbs are golden brown and the edges are bubbling, 1 to 3 minutes.
