Set your broiler to high. If you don't have a broiler, preheat the oven to 375 degrees.
Fill a large pot 3/4 the way with water and generously salt the water. (It should taste like the ocean!) Bring the water to a boil.
As the water comes to a boil, thoroughly dry the salmon fillets off with a paper towel.
Brush each salmon fillet with a thin layer of olive oil, until the fillet is fully coated. Squeeze some lemon juice over each salmon fillet (as much or as little as you want.)
Once the salmon is fully coated in olive oil and lemon, season each fillet with a pinch of salt, a pinch of pepper, and enough sesame seeds to fully coat the top of the fish. Use any extra seeds to coat the sides of the salmon.
Set the salmon aside. Once the water in the pot is boiling, it's time to blanch your broccoli.
Put all of the broccoli florets into the pot of boiling water and let them boil for 1-1.5 minutes. Remove the broccoli from the water with a colander or slotted spoon, letting excess water drain from the broccoli. Then place the relatively dried off broccoli onto a sheet pan.
Drizzle olive oil onto the broccoli florets and toss them until fully coated. Sprinkle with salt and pepper and spread the florets onto 2/3 of the sheet pan, leaving some space for the salmon fillets.
Place the salmon fillets on the other side of the sheet pan, Put the sheet pan on the 3rd highest rack in your oven, and let it broil for 8-10 minutes.