• Place the salt, sugar, garlic, peppercorns, thyme and 4 cups of hot water into a pot large enough to hold the breasts plus 12 cups of water. Heat the water and seasonings until the salt and sugar is dissolved. Remove from heat and add 8 cups of cold water. Once the brine has come to room temperature add the turkey breasts and refrigerate overnight.
• 2 hours before cooking remove breasts from the brine. Rinse well and pat dry with paper towels. Discard brine. Let the turkey sit for 2 hours to come to room temperature before cooking.
• Preheat oven to 425°F. Place a cast iron skillet or another ovenproof frying pan over high heat. When hot add 1 tablespoon of olive or avocado oil to the pan, then add the turkey breasts, skin side down, and reduce the heat to medium-high. Cook for 4-5 minutes or until nicely browned. Check the skin to make sure it isn't burning. If getting too dark, reduce the heat.
• Using tongs, flip the breasts so they are skin-side up and place in the preheated oven. Bake for 15-20 minutes or until temperature, with a quick read thermometer, registers 160°F at its thickest part. Remove from the oven and place breasts on a plate or platter. Tent loosely with foil and let rest for 10 minutes before slicing. Slice against the grain (crosswise) on the bias.

Making the Gravy

• Heat oil in a medium to large saucepan over medium-high heat. Add chopped onion, carrot, celery, garlic, salt and pepper. Stirring every so often, cook vegetables until they are softened and starting to brown. Adjust heat as necessary. Add flour, stir and cook for 1 minute. Add thyme sprigs. Slowly add chicken broth, stirring constantly and scraping up the brown bits from the bottom of the pan. Bring to a boil and reduce heat to a simmer. Let simmer for 15 minutes or until thickened and reduced. Strain sauce with a fine mesh strainer. Taste and add salt and pepper as needed.