Preheat the oven to 350 degrees F with 2 sheet pans on the center racks.
Stir together the panko breadcrumbs, almonds, 1/4 teaspoon kosher salt, 1/4 teaspoon black pepper and 1 tablespoon olive oil in a glass pie plate. Toast in the oven until lightly golden, about 12-15 minutes. (You can just put the pie plate on one of the sheet pans).
Increase the oven temperature to 400 degrees F.
In a large bowl, whisk together the mustard, honey, balsamic vinegar, 2 tablespoons olive oil, garlic powder, red pepper flakes, 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper. Stir them the brussels sprouts in the mixture.
Remove the preheated sheet pans from the oven. Spread the brussels sprouts across both pans.
Roast for 15-20 minutes using a spatula to flip and toss the sprouts about halfway through cooking. They should be lightly browned and crisp at the edges.
Sprinkle the brussels sprouts with the breadcrumbs, parsley and grated parmesan. Toss to coat.