Preheat the oven to 400°F. Allow the salmon to come to room temperature (or brine it in Step 2).
Brine the salmon (optional): While the oven preheats, in a shallow dish mix together 4 cups room temperature water and 3 tablespoons kosher salt. Place the salmon in the water and wait for 15 minutes (this should be about the time it takes to preheat).
Place a large sheet of aluminum foil on a baking sheet and brush it with olive oil. Pat each piece of salmon dry and place it on the foil skin side down. Brush with olive oil. Sprinkle the salmon with the kosher salt evenly divided among the fillets.
In a medium bowl, mix together the brown sugar, paprika, garlic powder, onion powder, thyme, and cumin. Sprinkle the mixture evenly on top of the fillets.
Bake the salmon for 10 to 16 minutes, depending on thickness, until just tender and pink at the center (the internal temperature should be between 125 to 130°F in the center). A 1-inch thick fillet should cook in about 15 minutes total. For a crispy top, when the salmon is at 115°F, broil for about 2 minutes (about the last 2 minutes of the cook time).