In a medium bowl, combine potatoes and brussels sprouts. Mix in 1 tablespoon olive oil, salt, and pepper to taste. Mix well and place in a single layer on baking sheet. Bake in oven for about 25-30 minutes or until potatoes are soft and starting to brown.
When vegetables are about 5-10 minutes from being finished, heat a large skillet under medium high heat and add remaining olive oil.
Combine salt, pepper, garlic, thyme, basil, paprika, parsley, and lemon juice. Pour mixture on top of each trout fillet and gently rub in, if desired.
Place trout, skin side down, in skillet and cook for about 4 minutes, or until skin is nice and golden brown. Carefully flip over and cook an additional 2 more minutes, or until fish is white throughout.