Preheat the oven to 425℉/218℃. Line a large baking sheet with parchment paper and brush it with a thin layer of olive oil. Set aside.
Fill a large pot with a couple inches of water. Bring to a boil over high heat. Place a vegetable steamer basket in the pot (or fine mesh strainer if you don't have a steamer). Add the Brussels sprouts. Cover and steam for 10 to 15 minutes until they can be easily pierced with a fork but are not falling apart. Do not over cook. Carefully remove the basket from the pot.
On the prepared baking sheet, sprinkle a couple tablespoons of parmesan roughly in the areas of the three rows where you will arrange the Brussels sprouts.
Transfer the steamed Brussels sprouts to the baking sheet and spread them out on top of the parmesan rows in a single layer so they're not overlapping. Smash each one with the bottom of a drinking glass or glass jar to flatten them.
In a small bowl, combine the rest of the olive oil, lemon zest, red pepper flakes, and salt. Brush this mixture onto the sprouts. Sprinkle each sprout with the remaining parmesan cheese.
Transfer the sprouts to the center rack of the preheated oven. Bake for 18 to 23 minutes until browned and crispy on the outside yet tender on the inside.
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Notes
Brussels sprouts tips: This recipe works best with small sprouts (1 to 1.5 inches in diameter) with tightly packed leaves. If you have bigger sprouts, cut them into smaller pieces.
Parchment paper: Some of my other smashed vegetable recipes call for no parchment paper, but I have found that using parchment for Brussels sprouts in particular helps prevent them getting burnt and stuck on the pan.
Steaming vs. boiling: If you don't have a steamer basket or fine mesh strainer, you can boil the Brussels sprouts in a pot or skillet with water. Cook for just 3 to 5 minutes until fork-tender. Drain well and pat dry.
Storage and reheating: Keep in an airtight container in the refrigerator for 2 to 3 days. To restore crispiness, reheat in a skillet with a little oil for a few minutes on each side until warm. To reheat in the oven, preheat to 400 degrees F/204 degrees C and place the sprouts on a baking sheet on the center rack. Cook for 5 to 10 minutes until warm.