How to Make It
Preheat the oven to 350°. Lightly brush a medium, shallow baking dish with olive oil. In a large skillet, heat 3 tablespoons of the olive oil. Add the minced garlic and the onion and cook over moderately low heat until softened, about 4 minutes. Add the mushrooms and season with salt and pepper. Cover and cook over moderately low heat until softened and just golden, about 7 minutes. Add the shrimp and cook, stirring, just until opaque, about 2 minutes. Stir in the flour and then the milk and bring to a simmer, stirring, until smooth. Stir in the parsley, bread crumbs and pimentón and season with salt and pepper. Stir in the egg yolks and remove from the heat. Continue to stir until the egg yolks are fully incorporated and the stuffing is thick, 1 to 2 minutes. Let cool.
Make a lengthwise slit down 1 side of each piquillo pepper. On a work surface, open the peppers and spoon the stuffing into the center, overfilling them slightly. Close the pepper around the stuffing as neatly as possible. Transfer the stuffed piquillo peppers to the prepared baking dish, seam side down, and bake for about 15 minutes, or until they are heated through.
Meanwhile, in a small skillet, heat the remaining 1 tablespoon of olive oil. Add the sliced garlic and cook over low heat until golden, about 3 minutes. Add the tomatoes and cook over moderate heat, stirring occasionally, until a thick sauce forms, about 12 minutes. Season with salt and pepper.
Using a spatula, carefully transfer the stuffed piquillos to plates. Spoon the tomato sauce over them and serve.