Prepare the venison: A venison rack often has a little silverskin running down the loin that you can remove with a paring knife, leaving the loin of the rack bare. There is no fat on the venison rack, so it will cook rather quickly, and you don’t want to cook it too aggressively. You should french the bones as well, cutting away any of the rib meat from between bones: Using the bones as your guide, slide your knife down the side of one bone and then along the top of the loin and up the other bone. Once you’ve removed all the rib meat from between the bones, scrape all the meat from around the bones. And letting your meat come to room temperature will allow it to cook much better.
Preheat the oven to 350°F (175°C). In a castiron pan set over medium high heat, heat the oil. Season the venison with salt and pepper, then place it loinside down in the middle of the pan. Sear until it’s golden brown, then flip the rack so the bones are against the side of the pan and sear the bottom. Then, using tongs, flip the venison on its side, holding it straight up, and sear both sides.
Place the venison on a baking sheet and roast in the oven five minutes; tent with aluminum foil and let rest 15 minutes. Set the castiron pan over medium heat. Add the butter, garlic, rosemary, and thyme; let it get frothy. Return the venison to the pan, with the bones leaning against the edge. Tilt the pan so the butter pools; baste the venison three minutes with the frothy, garlicky herbed brown butter. Transfer the venison to a cutting board and pour the butter garlic goodness all over it.
Make the sauce: In the same pan, add the vinegar and sugar and deglaze, swirling with a wooden spoon. Let it start to caramelize and really bubble, then add the port, Madeira, and espresso grounds and reduce by half, 10 minutes. Add the demiglace and the chocolate, swirling constantly, with the pan handle (wrapped in a kitchen towel) in one hand and the wooden spoon in the other. Remove the sauce from the heat and add some pepper and a squeeze of lemon juice, if needed. Carefully pour the sauce through a fine chinois into a saucepot. Stir in the butter until melted (the sauce should still be hot). Slice the venison rack between the bones into perfect medium-rare chops. Pool the sauce on the bottom of a warm plate and place the venison chops on top.