
Prepare the Rice Filling
In a saucepan, heat a drizzle of oil over medium heat. Add the shallots and sauté for a few minutes until softened. Add the mushrooms and cook together until tender and lightly browned.
Stir in the garlic, raw rice, liquid, and spices. Bring to a boil.
Cover and reduce to a simmer. Cook for 20–25 minutes, until the rice is tender and the liquid is absorbed. Set aside to cool slightly.
Assemble the Capons
Preheat the oven to 375°F.
Lay the capons flat. Place about 2 tablespoons of the rice filling in the center of each piece. Roll up tightly and place seam-side down in a baking dish. Repeat until all are stuffed.
Make the sauce:
In a bowl, whisk together all of the sauce ingredients until combined. Pour evenly over the stuffed capons.
Cover tightly and bake for 1 hour. Uncover and bake for an additional 30 minutes, until the tops are golden and the sauce has thickened.