2 large (12-ounce) heads broccoli
¼ cup olive oil, plus additional for cooking
2 teaspoons minced garlic
¼ cup minced shallots
5 anchovy filets, rinsed, patted dry and minced
1 cup panko bread crumbs
1 tablespoon grated lemon zest
¼ cup finely chopped flat-leaf parsley
Lemon slice, for serving
Cut the bottom 2-inches of the stem off of the broccoli and discard. Hold the broccoli on a parchment paper-lined cutting board. The parchment paper will make gathering all the tiny pieces of excess broccoli easier. With the stem pointing to the ceiling, use a paring knife or peeler to peel the skin off the stem. Place the broccoli flat (head and stem) on the cutting board. Trim the broccoli head on one side and then the other, so that it makes a straight line with the stem of broccoli. Place the broccoli head down, with the stem towards the ceiling again, and cut lengthwise through the stem and then the head to create ¼-inch slices of broccoli that look like trees. Reserve the excess broccoli florets for use in the gratin.
Line a small baking sheet with parchment paper; set aside.
Set a medium sauté pan over medium heat. Add ¼ cup olive oil. Add the garlic and shallots, lightly season with salt and pepper, and sauté until light golden brown, about 2-3 minutes. Turn down the heat to medium-low and stir the minced anchovy into the sauce and aromatic, about 30 seconds more. Stir in the breadcrumbs, season with salt and pepper, and cook, stirring continuously, until the golden brown, about 5 minutes. Turn off the heat, add the lemon zest and parsley. Taste and season with more salt and pepper, as needed.
Transfer the gremolata to the parchment-lined baking sheet to completely cool.
Heat a grill pan or outdoor grill over medium-high heat and preheat the oven to broil. Brush each slice of broccoli all over with grapeseed oil and season with salt and pepper. Brush the grill grates with grapeseed oil. Grill, in batches if needed, the slices of broccoli on both sides until char marks appear and a cake tester (or a paring knife) can easily be inserted into the broccoli stem, about 3-4 minutes per side. Transfer to a baking sheet lined with a rack. Spoon the breadcrumb mixture on top of each grilled broccoli slice and transfer to the oven and cook under broil for approximately 30 seconds to 1 minute. Note: If the stems of the broccoli are not tender after grilling, place broccoli with gremolata in an oven at 425°F for 5-10 minutes. Squeeze with lemon and serve.