Step 1: Begin by brining your wild turkey breast. In a large bowl or container, dissolve 1/4 cup salt and 1/4 cup sugar in 4 cups of warm water. Add 2 cups of ice water to cool it down. Submerge the wild turkey breast and refrigerate for at least 4 hours, or up to 8 hours.
Step 2: After brining, remove the turkey breast and pat it thoroughly dry with paper towels.
Step 3: In a small bowl, combine 4 cloves of minced garlic, 2 tablespoons chopped fresh rosemary, 2 tablespoons chopped fresh thyme, 1 tablespoon chopped fresh sage, 1/4 cup olive oil, 1 teaspoon black pepper, and 1/2 teaspoon smoked paprika. Mix well.
Step 4: Generously rub the herb mixture all over the wild turkey breast, ensuring it's evenly coated. Let it sit at room temperature for 30 minutes while you preheat your oven.
Step 5: Preheat your oven to 400°F (200°C). Heat 1 tablespoon of olive oil in an oven-safe skillet over medium-high heat. Once shimmering, sear the wild turkey breast for 3-4 minutes per side, until deeply golden brown.
Step 6: Transfer the skillet to the preheated oven. Roast for 15-25 minutes, or until an instant-read meat thermometer inserted into the thickest part of the breast registers 160°F (71°C).
Step 7: Remove the skillet from the oven and transfer the wild turkey breast to a cutting board. Tent it loosely with foil and let it rest for at least 10-15 minutes.
Step 8: Slice the wild turkey breast against the grain into 1/2-inch thick pieces. Serve immediately with your favorite sides.