Step 1

Trim 1" from bottom of broccoli stems, then peel. Remove stalks from crowns; set crowns aside for another use. Cut stalks in half lengthwise and set aside.

Step 2

Finely grind fennel seeds in spice mill or with mortar and pestle. Transfer to a small bowl and mix in sugar.

Step 3

Season pork chops all over with salt, then rub with fennel mixture. Let sit at room temperature 30 minutes, or, if you have the time, chill overnight.

Step 4

Pour 2 Tbsp. oil in a large cast-iron skillet over medium-high. Cook pork chops, without moving around but pressing down with tongs to ensure meat is in direct contact with pan, until golden brown underneath, about 2 minutes. Turn pork chops over and cook until other side is golden brown, about 2 minutes. Continue to cook, turning about every minute or so, until chops are deep golden brown on both sides and an instant-read thermometer inserted into the thickest part registers 135°, 6–8 minutes. Transfer pork chops to a cutting board and let rest 10 minutes before serving. Reserve skillet.

Step 5

There should still be some oil in reserved skillet; if not, add 1 Tbsp. oil and place skillet over medium-high. Add broccoli stems and cook until lightly charred, about 2 minutes per side. Transfer to a cutting board and let cool 3 minutes, then coarsely chop (about ½" pieces).

Step 6

Transfer broccoli pieces to a medium bowl and add garlic, olives, parsley, vinegar, lemon zest, and remaining ¼ cup oil. Toss well to combine and season broccoli salsa verde with salt and pepper.

Step 7

To serve, carve pork chop meat away from bones, then slice meat against the grain ½" thick. Divide slices among plates and spoon some broccoli salsa verde on top.