For the filling: In a medium pot, heat the olive oil over medium heat. Add the spinach and cook, stirring constantly, until just wilted, about 2 minutes. Add the cheese, garlic and red pepper flakes. Cook over medium heat, constantly tossing and stirring, until the cheese melts and everything is mixed together, another 2 to 4 minutes. Season lightly with a pinch of salt and a few grinds of pepper.
For the topping: In a food processor, add the breadcrumbs, walnuts, a pinch of salt and a few grinds of pepper. Pulse to combine, then, with the motor running, slowly drizzle in the olive oil. The mixture should be crumbly and easy to sprinkle.
For the mushrooms: Stuff each mushroom with an equal amount of the filling. Sprinkle an equal amount of topping over each mushroom. Place on a baking sheet and bake until the tops are golden and the mushrooms are cooked through, 8 to 10 minutes.