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Step 1
Preparation Combine brown sugar, black pepper, and 2 Tbsp. kosher salt in a small bowl. Place turkey legs in a baking dish just big enough to fit them or a medium Dutch oven. Sprinkle all over with brown sugar mixture and scatter smashed garlic cloves around. Let sit at room temperature at least 2 hours, or chill up to 12 hours (more time makes a big difference).
Step 2
Place a rack in middle of oven; preheat to 275°F. Cut heads of garlic heads in half crosswise. Nestle around turkey legs along with chiles and oregano sprigs. Pour in oil until turkey is mostly if not completely submerged (shove chiles down since they can burn if above the surface of the oil). You may need a bit more oil depending on your pot and size of turkey legs; don’t worry, this oil can be reused in all kinds of ways so it won’t go to waste!
Step 3
Braise turkey, uncovered, until meat has shrunk away from drumsticks dramatically and meat shreds easily with firm pressure, 3–4 hours (a few bubbles is okay, but anything above a lazy simmer and you should reduce the heat). Let meat rest, still submerged in fat, at least 1 hour.
Step 4
Pick out chiles from braising oil with tongs and place in a blender; add red pepper flakes and 1 cup braising oil. Let cool slightly, then blend until chiles are coarsely chopped. Add almonds and pulse until largest pieces are no bigger than a red pepper flake. Add sesame seeds and pulse just to combine. Season with remaining ¼ tsp. salt and add more red pepper flakes if desired.
Step 5
If eating right away, heat 2 Tbsp. braising oil in a large nonstick or cast-iron skillet over medium heat. Cook turkey legs, carefully turning with 2 pairs of tongs, until brown and crisp all over, 8–10 minutes. Serve with the almond-chile sauce.
Step 6
Don’t discard the braising oil or the juices below: Strain through a fine-mesh sieve into a heatproof container. Skim off fat to use for roasting potatoes, or your next confit project. Use juices in another braise, or stir into a pot of beans.
Step 7
Do ahead: Turkey can be braised 4 days ahead. Let cool, cover and chill (still in oil). Reheat, uncovered, in a 275°F oven until warmed through, about 40 minutes, before browning.