1 1/2 pounds ground beef chuck (20% fat)
2 tablespoons chopped parsley
2 large garlic cloves, finely chopped, divided
1 1/2 teaspoons paprika, divided
5 tablespoons (or more) unsalted butter, divided
1/4 cup tomato paste
4 hamburger or brioche buns
1 tablespoon vegetable oil
2 teaspoons kosher salt
1 teaspoon freshly ground black pepper
Step 1: Preheat oven to 400°F. Mix beef, parsley, half of garlic, and 1 tsp. paprika in a large bowl.
Step 2: Divide into 4 loosely packed patties 4" wide and 3/4" thick.
Step 3: Make a small indentation in the center with your thumb to help keep it flat as it grills. Chill until ready to use.
Step 4: Meanwhile, cook 4 Tbsp. butter and remaining garlic in a medium saucepan over medium heat, swirling pan occasionally, until butter turns caramel-brown and smells nutty, about 5 minutes.
Step 5: Add tomato paste and remaining 1/2 tsp. paprika, whisk to combine, and cook until paste begins to caramelize, about 30 seconds.
Step 6: Add 3/4 cup water and whisk until smooth; simmer until mixture thickens slightly, about 5 minutes. Remove from heat.
Step 7: Heat a large skillet over medium-high. Melt 1 Tbsp. butter and cook buns, cut side down, until cut sides are golden-brown, about 2 minutes (you may need to do this in 2 batches, using additional butter if needed).
Step 8: Using a brush, generously brush cut side of buns with tomato sauce. Transfer buns to a 13x9" glass baking pan.
Step 9: Add oil to skillet and increase heat to high; heat until oil begins to smoke.
Step 10: Season patties on both sides with salt and pepper. Reduce heat to medium and cook burgers until lightly charred on the bottom, 2–3 minutes.
Step 11: Flip and cook to desired doneness, 2–3 minutes for medium-rare.
Step 12: Transfer burgers to pan with sauce and coat burgers in sauce.
Step 13: Transfer burgers to bun bottoms and top with top bun. Brush top of bun with sauce.
Step 14: Cover pan with parchement paper, transfer to oven, and bake 5 minutes.
Step 15: Carefully remove paper and serve immediately. Raw burger patties and sauce can be made 3 days ahead; cover separately and chill. Reheat sauce in a medium saucepan over medium, whisking until smooth.