Preheat the oven to 375 degrees Fahrenheit.
Clean 6 portobello mushrooms by wiping them with a damp cloth.
Gently remove the stalk from the center of the mushroom.
Use a spoon to scrape out the gills from each mushroom (reserve the gills to add to the stuffing mixture).
Use a basting brush to coat the tops and sides of the mushrooms with 1 tablespoon of extra virgin olive oil, making sure that all of the areas that won’t be stuffed are thoroughly coated with oil.
Add the gills from the mushrooms, 2 chopped garlic cloves, 1/2 cup fresh basil, 1/2 cup fresh parsley, 3/4 cup walnuts, 1/2 cup gluten-free oat flour, 1/4 cup extra virgin olive oil, 3/4 teaspoon salt, and 1/4 teaspoon black pepper to a food processor and process with several quick on/off pulses until everything is thoroughly mixed (alternatively, you could finely chop all the ingredients by hand and stir in a mixing bowl).
Spoon the stuffing mixture into the mushrooms, making sure they are full but not overflowing.
Bake at 375 degrees Fahrenheit for 40 minutes.