Smashing Brussels sprouts before you roast them results in extra surface area, which translates to more crispy cheesy bits. If you have a meat mallet, it makes the smashing particularly easy and fun, but you can also use a cast-iron skillet or heavy drinking glass or mug.
Preheat the oven to 425 degrees F with a sheet pan on the bottom rack.
Bring a large pot of salted water to a boil. Add the Brussels sprouts and boil until tender throughout, 10 to 12 minutes. Drain in a colander and cool under running water. Pat very dry with kitchen towels.
Flatten each sprout with a meat mallet. Transfer to a large bowl and toss with 1/2 cup of the manchego, the olive oil, smoked paprika, garlic and 1 teaspoon salt. Spread on the preheated sheet pan and roast until crispy on the bottom, 13 to 15 minutes.
Flip the sprouts and sprinkle with the remaining 1/2 cup manchego. Roast until the tops are browned and crusty and the bottoms are deeply caramelized, 13 to 15 minutes more.
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