Preheat the oven to 400°Farenheit (200°Celsius).
Season both sides of the chicken breasts with salt, pepper, and garlic powder.
Heat 1 tablespoon of olive oil in a large oven-safe skillet with a lid or a Dutch oven over medium heat until shimmering.
Add the chicken breasts, skin side down, and cook without moving for 5 minutes until golden brown.
Flip the chicken over and add 3 tablespoons of butter to the skillet along with the crushed garlic. Let the butter melt and cook the garlic, then baste the chicken with the garlic butter using a large spoon.
Cook for 3 minutes, then remove the chicken from the skillet and set aside on a plate.
Reduce the heat to medium-low and add the remaining 3 tablespoons of butter and 1 tablespoon of olive oil to the skillet. Add the sliced leeks and shallot and sauté until fragrant, about 3-4 minutes.
Add the pearl couscous to the skillet and toast it with the leeks and shallots for 1-2 minutes.
Pour in the chicken broth and lemon juice, scraping up any browned bits from the bottom of the skillet. Crumble the feta cheese over the couscous mixture and stir to combine.
Nestle the seared chicken breasts on top of the couscous mixture. Cover the skillet with an oven-safe lid or foil.
Transfer the skillet to the preheated oven and bake for 25 minutes.
Remove the lid and return the skillet to the oven. Cook for an additional 5-7 minutes or until the broth is mostly absorbed and the couscous is fluffy and chewy.
Let the chicken rest for 5-10 minutes before slicing.
Serve the chicken and couscous hot, garnished with additional feta cheese and fresh herbs if desired.