Step 1

Heat a large Dutch oven over medium-high until hot. Divide beef into 4 large loosely packed balls and place in Dutch oven. With a sturdy spatula, aggressively flatten balls as though you were making smash burgers; season with salt. Cook, undisturbed, until patties are well browned and crisp on the bottom, about 4 minutes. Turn each patty, season with salt, and continue to cook until second side is well browned, about 3 minutes longer. Transfer patties to a plate and let cool slightly.

Step 2

Reduce heat to medium. Cook onion in pot, stirring often, until golden and browned around the edges, 10–15 minutes. (Some light scorching and sticking is okay here; don’t be shy.)

Step 3

While onions are cooking, transfer patties to a cutting board and coarsely chop.

Step 4

Add garlic to pot and cook, stirring, until fragrant, about 30 seconds. Using a wooden spoon or spatula, push onion-garlic mixture to one side of pot to make space, tilting pot if necessary to get some hot fat over to the empty side. Add tomato paste to empty space and stir in hot fat until fragrant and begins to darken, about 2 minutes. Add tomatoes, banana peppers, soy sauce, red pepper flakes, and chopped meat and stir everything in pot together. Cook, stirring occasionally, until sauce is simmering and flavors have melded, about 10 minutes. Reduce heat to low and keep warm until ready to use.

Step 5

Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until 1 minute shy of al dente (pasta will finish cooking in the sauce). Increase heat under sauce to medium. Using a spider or large slotted spoon, transfer pasta to Dutch oven along with 2 cups pasta cooking liquid. Stirring constantly, add cheddar and 3 oz. Parmesan a handful at a time, allowing cheese to melt and emulsify into sauce between additions, about 3 minutes.

Step 6

Transfer pasta to a platter. Top with more Parmesan.