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Step 1
Preheat the oven to 425 degrees F or start a wood burning oven.
Step 2
For the duck: Score the duck breast in a 1/4-inch cross hatch, salt the skin and allow to sit skin-side down on a tray for 25 minutes.
Step 3
To cook the duck breasts, pat the skin dry and place the breasts skin-side down in a large cast-iron skillet over medium-low heat. Begin to render the fat out of the skin. Allow the duck to roast for 18 to 20 minutes. Once the skin is golden brown, turn and tap the flesh side on the pan for a quick second, then return to the skin side and put into the hot oven for 2 to 3 minutes. Remove the duck breasts from the pan and allow to rest for10 minutes before slicing into 1/2-inch-thick slices.
Step 4
For the potatoes: Place the cast-iron pan back over medium heat and add the thyme and fingerling potatoes. Once they begin to get color on them, after a couple of minutes, finish the potatoes in the oven and allow to cook until golden brown, about 20 minutes. Remove the potatoes from the pan and set aside on a plate.
Step 5
For the jus: Add the duck stock and thyme to the pan, return it to the oven and allow to cook for 8 to 10 minutes. Pull the pan out of the oven and swirl in the butter and salt.
Step 6
For the vinaigrette: Add the orange juice, vinegar, Dijon, miso and thyme to the carafe of a high-speed blender. With the blender on, stream in the olive oil and grapeseed oil. Add the salt and pepper and set aside in a bowl. Fold in the sliced kumquats and cayenne and set aside.
Step 7
To serve: Line a platter with the radicchio and endive leaves. Place the sliced duck breasts over top of the chicories and top with the roasted potatoes and jus. Drizzle some of the vinaigrette over the platter and garnish with orange zest.