Preheat your oven to 350°F (180°C). Clean the hare legs, then season them generously with salt and pepper on both sides.
In a large skillet, heat the olive oil over medium-high heat. Sear the hare legs until golden brown on all sides. Remove from the skillet and set aside.
Add the finely chopped shallots and garlic to the skillet and sauté until softened and translucent.
Pour in the white wine and cook until the liquid has reduced by half. Add the chicken stock and fresh thyme.
Place the hare legs in a baking dish. Pour the wine and stock mixture over them. Cover with foil and bake for 1 hour.
Prepare the mustard sauce: melt the butter in a small saucepan, add the Dijon mustard, and then whisk in the heavy cream. Simmer over low heat until the sauce thickens slightly.
Remove the hare legs from the oven and drizzle generously with the mustard sauce. Serve with mashed potatoes or steamed vegetables.
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