In a bowl, combine the mustard, 2 tablespoons of the oil, the garlic, thyme, vinegar, marjoram, salt and pepper and mix well. Rub the fish with 1/2 teaspoon of the oil and place in a roasting pan, skin-side down. Brush the mustard mixture onto the fish and lay the lemon slices over the top. Drizzle with the remaining 2 1/2 teaspoons oil and roast until the fish is cooked through, about 20 minutes.
In a large saute pan or skillet, heat the oil over medium heat. Add the garlic and cook, stirring, until fragrant and starting to turn golden, 1 1/2 to 2 minutes. Add the lemon juice, salt and pepper flakes and stir to combine. Add the broccoli and cook until warmed through and coated with the oil mixture. Adjust the seasoning to taste.
Toss with the Parmesan and serve immediately.