Bring 1/2 cup of water to a boil and stir in 1/4 cup of the uncooked quinoa. Cover, turn the heat to low and cook until all the water is absorbed (about 15 to 20 minutes). Set aside to let the quinoa cool.
Preheat your oven to 400°F and lightly grease a baking sheet with cooking spray. Set aside.
Place the remaining 1/4 cup of uncooked quinoa into a spice grinder or food processor and process until ground into a fine flour. Pour the quinoa flour into a large, shallow plate.
Transfer the cooled, cooked quinoa into a large bowl and add in 1/4 cup of the grated goat cheese, the Italian seasoning, garlic powder, and season to taste with salt and pepper. Mix well and pour into a large, shallow plate.
Place the egg white on a large shallow plate.
Pat each chicken breast dry, then dredge in the quinoa flour, pressing to get it evenly coated. Then, transfer each breast into the egg white, also making sure to evenly coat it. Finally, transfer the breasts into the cooked quinoa/cheese mixture, really making sure to coat each side. You will really have to press the quinoa to make it stick.
Place the breasts onto the prepared baking sheet and lightly spray with cooking spray.
Bake until lightly golden brown and crispy, about 20 to 25 minutes.
Turn your oven to high broil, sprinkle the remaining 1/4 cup of grated cheese on the chicken, and broil until melted, about 2 minutes.
Garnish with sliced roasted red peppers and basil.