Wash and dry all produce. Preheat oven to 425 degrees. Halve, peel, and thinly slice onion. Slice tomatoes into rounds. Split buns in half. Shape beef into four evenly sized patties (they should be slightly wider than the buns).

Toss broccoli on a baking sheet with a large drizzle of olive oil and a pinch of salt and pepper. Roast in oven until slightly crispy, about 15 minutes.

Heat a large drizzle of olive oil in a large pan over medium-high heat. Add onion and cook, tossing, until soft, 5-6 minutes. Stir in sherry vinegar and 2 tsp sugar. Simmer until liquid is nearly evaporated, 1-2 minutes. Season with salt and pepper. Transfer to a small bowl and set aside.

Line another baking sheet with parchment paper. Place cheddar on it in four even piles. Bake in oven until melted in middle and crispy at the edges, 5-7 minutes. TIP: If you don’t have parchment, that’s OK. As soon as the frico come out of the oven, transfer to a plate to cool using a spatula.

Meanwhile, heat a large drizzle of olive oil in same large pan over medium-high heat. Season patties all over with salt and pepper. Add to pan and cook to desired doneness, 3-6 minutes per side. Meanwhile, carefully remove frico from baking sheet. Discard parchment paper and place buns on sheet. Toast in oven until golden, 3-4 minutes.

Fill each bun with a burger, onion jam, tomato slices, ketchup, and a frico. Serve with broccoli on the side.