Preheat the oven’s broiler. Place an oven rack about 6 to 8 inches beneath the broiler.
Line a sheet pan with foil first and brush with 1 Tbsp of cooking oil.
Make spice blend: While oven is heating combine brown sugar, smoked paprika, thyme, salt, garlic powder, dried oregano, black pepper, and cayenne. Set aside.
Make salsa verde: Make the salsa verde by combining all of the ingredients in a food processor or blender (or use an immersion blender) and blend until evenly combined and only small flakes of the herbs remain. You can also finely chop everything by hand.
Score and season salmon. Place salmon on prepared sheet pan, skin-side down. Use a sharp knife to cut / score the salmon a few times. (Note: Focus the slices on the thickest part of the salmon and slice to a depth that is about halfway through the salmon filet. This step will help the salmon to cook more quickly in the thick spots and will allow some of the flavor to reach the center of the fish.)
Brush or rub salmon with remaining 2 Tbsp of cooking oil and then rub the spice blend into the top of the fish, including getting some of the spices down into the slices you made.
Broil salmon: Broil until salmon is golden brown on top and flakes easily with a fork, 8 to 15 minutes, depending on thickness. (Keep an eye on your oven. Oil from the salmon can sputter up as it cooks and will occasionally cause smoking. I turn on the kitchen fan before I begin just to get ahead of any smoke that may form.)
Serve salmon immediately with salsa verde on top.