Heat the olive oil in a large pot with a lid over medium heat until shimmering. Add the onion and garlic and sauté for 2 minutes, until translucent.
Add the ground beef and cook until browned, about 7-10 minutes.
Add the crushed tomatoes, tomato paste, brown sugar, salt, ground pepper, paprika, chili powder, ground cumin, and stir to combine. Add water and stir. Bring to a boil, then reduce the heat to low, cover, and simmer for 30 minutes.
Set a wire cooling rack on top of a baking sheet. Place a metal 1-cup (240 ml) measuring cup upside down on top of the cooling rack.
In a medium non-stick skillet over medium heat, pour ⅓ cup (35 g) of Parmesan in the center of the pan and spread out into a thin circle, about 5 inches across. Without disturbing the cheese, melt for 2-3 minutes, or until golden and fully melted.
Once the cheese is fully melted, run a spatula along the edges of the cheese and shake the pan to loosen the cheese circle. Carefully slide the melted cheese over the inverted measuring cup to form a cheese bowl. DO NOT TOUCH, it is extremely hot. Set aside and let cool completely, about ten minutes. Repeat with the rest of the Parmesan to make 8 bowls.
Lightly grease a large skillet over high heat, then add the beef patties (in batches, if necessary) and season generously with salt and pepper. Cook for 2 minutes without disturbing, then flip and cook for another 3 minutes, or until the internal temperature has reached at least 165˚F (75˚C).
To assemble, place a bottom burger bun on a plate and put a cheese bowl on top. Lay a burger patty inside the cheese bowl and top with a spoonful of chili, a sprinkle of shredded cheddar cheese, and the top bun.
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