In a large pot, bring water to a boil and season. Submerge the broccoli, head side down, into the boiling water. Boil for 4-5 minutes, just until the broccoli begins to soften. Once done, transfer the broccoli to a colander to drain and cool.
Prepare the garlic-infused olive oil. Brush a baking sheet with some of the oil. Break broccoli into florets and slice the stem thinly. Pat the florets and stem dry using paper towels. Arrange them on the prepared baking sheet.
Using the bottom of a jar, gently press down on each broccoli floret to smash them. If they stick to the jar, gently separate them using a spatula.
Brush the smashed broccoli with the garlic-infused olive oil. Season with salt and pepper. Generously sprinkle grated Parmigiano over each floret.
Place the baking sheet in a preheated oven at 200°C / 400°F with a fan setting and bake for approximately 15 minutes, or until the broccoli develops golden brown spots.
Allow the broccoli to cool for about 5 minutes before serving. These can be enjoyed as an appetizer, snack, or side dish, either warm or cold.