Place a rack in the center of the oven and preheat the oven to 400 degrees. Line a large baking sheet with parchment paper or a silicone baking mat.
Lightly beat the eggs in a wide, shallow bowl or pie plate and set aside.
In a food processor, pulse the pecans until they form fine crumbs (but don't over-process or they will turn into pecan butter). Place the mixture in a large, sturdy ziptop bag.
To the bag, add the breadcrumbs, basil, salt, and pepper. Seal the top and shake to combine.
Place the chicken on a cutting board and cover it with a large sheet of plastic wrap. With a meat tenderizer, rolling pin, or your fist, pound the chicken breasts to an even thickness. They need not be super thin—just flatten the middle so that the chicken is relatively flat and will bake more evenly.
Working one chicken breast at a time, dip the chicken in the egg wash, then place in the ziptop bag and shake to coat with the pecan mixture. Gently press the pecan mixture so that it sticks to the chicken, then lay the chicken on the prepared baking sheet. Repeat with remaining chicken breasts.
Drizzle the olive oil over the top of the chicken. Bake until the chicken reaches 160 to 165 degrees F on an instant read thermometer, about 15 to 20 minutes. Remove to a plate and let rest 5 minutes. Chicken is considered cooked at 165 degrees F, but I like to remove mine several degrees early and let the carryover cooking to finish the rest (this ensures the chicken breast is juicy and does not overcook).
While the chicken bakes, prepare the sauce: In a small bowl, stir together the Greek yogurt, both mustards, honey, salt, and cayenne. Taste and adjust the seasoning as desired.
Enjoy the pecan crusted chicken hot, with the dipping sauce.
Notes
TO STORE: Refrigerate the chicken in an airtight storage container for up to 3 days.
TO REHEAT: Rewarm leftovers on a baking sheet in the oven at 350 degrees F.
TO FREEZE: Freeze chicken in an airtight freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.
A much older version of this recipe included a strawberry and goat cheese topping. We've since come to prefer the simplicity of the honey mustard dip. If you'd like to try this version: Heat 1 teaspoon olive oil in a small saucepan, then add 1 1/2 cups strawberries, 2 tablespoons balsamic vinegar, 1/4 teaspoon dried basil, and 1/8 teaspoon kosher salt. Bring to a simmer and cook, stirring occasionally, until thickened, about 10 minutes. Top baked chicken with strawberry sauce and crumbled goat cheese.