Pat the rainbow trout fillets dry with paper towels. Rub the fillets with olive oil, sprinkle with salt and freshly ground pepper. Add chili flakes if desired. Set aside.
Preheat oven to 425F. Place a rack in the middle of your oven.
Rinse broccoli, drain from water. On baking sheet add the broccoli, olive oil, salt and freshly ground pepper. Toss the broccoli with the oil and the seasonings and spread out on baking sheet.
Bake in the oven for 10 minutes. After 10 minutes of roasting, stir the broccoli and push it to one side leaving just enough space to add the trout fillets.
Place the fillets on the baking pan and return to the oven. Cook for another 10 minutes before checking fillets for doneness. You can do this by using a fork or the tip of a knife to flake the thickest part of the fish, if it flakes easily, the fish is done, if not return to the oven for a couple more minutes before checking again.
Start by making a garlic paste by crushing and mashing your garlic with a little bit of salt. If you don't own a mortar and pestle, you can also chop the garlic up really finely and then use the side of your knife blade to mash it and turn it into a paste.
In a small bowl, combine the lemon juice, garlic paste and salt. Add the tahini paste and slowly add 1/2 cup of water, whisking until the sauce is well blended. Taste and adjust to your liking. If the sauce is too thick, you can add a teaspoon of water at a time until you have reached the desired consistency.
If desired add the chopped parsley to the tahini sauce before serving.
To ensure the fish is cooked thoroughly, use a fork to flake the thickest part of it, if it flakes easily it's cooked, if not, return it to the oven and bake for a couple minutes more before checking again.