Trim the wild boar culottes and score the fat layer. Sear them in a hot pan until browned on all sides, then transfer to a Dutch oven or clay roasting pot. Add red wine, port, salt, pepper, and stock. Cover and roast at 350°F (180°C) for 1½ to 2 hours, until tender.

Meanwhile, peel the potatoes and cut them into thick fries. Soak in cold water for about an hour to remove excess starch. Drain and pat dry. Toss with oil and salt, then arrange on a baking tray lined with parchment—leave space between each fry. Scatter thyme sprigs on top and roast in the oven at 350°F (180°C) for about 45 minutes.

To prepare the Béarnaise-style sauce, whisk the egg yolks with a pinch of salt. Slowly drizzle in the warm clarified butter—start with a few drops, then a thin stream—until about half is incorporated. Add Béarnaise essence to taste, then finish whisking in the remaining butter until the sauce reaches a smooth, creamy consistency. Stir in fresh tarragon.

Slice the braised culotte and plate with the oven fries. Serve the sauce on the side.

Suggested pairing:
This dish goes beautifully with a raw celery root salad topped with salt-baked almonds and walnuts. Almost any hearty winter vegetable can stand alongside it.