Step 1

Slice off the top of 1 onion to create a flat bottom. Slice into quarters through the center of the root end. Peel off the skin. Repeat with the second onion.

Step 2

Bring a heavily salted pot of water to a boil. Boil onion quarters until layers start to soften and separate, 8 to 10 minutes. Remove onions with a slotted spoon and place, cut-sides down, on a baking sheet lined with paper towels. Let drain and cool.

Step 3

Set an oven rack about 6 inches from the heat source and preheat the oven's broiler.

Step 4

Heat a medium pan over medium heat. Add bread crumbs and 1/8 cup olive oil; toss with a wooden spoon until golden brown, about 5 minutes. Add garlic, salt, pepper, cayenne, and 1/4 cup Parmigiano-Reggiano cheese. Mix until completely combined.

Step 5

Cut root end off the onions and separate the petals. Coat a 10- to 12-inch round pan with a drizzle of olive oil. Arrange onion petals in concentric circles around the pans. Do not overlap petals by much. Scatter bread crumbs into the petals. Sprinkle remaining Parmigiano-Reggiano on top, and add a drizzle of olive oil.

Step 6

Broil until browned and crispy, 5 to 10 minutes. Let cool to room temperature before garnishing with parsley and serving.