Preheat oven to 210 degrees Celsius or 400 degrees Fahrenheit.
Peel and chop potatoes into 1-inch chunks. Peel carrots and cut into 1-inch chunks. Horizontally halve carrots that are 1-inch or more in diameter. Cut off dark green leaves from leeks, and slice off root ends. Peel off top layer of leeks, and rinse. Cut into 2-inch chunks, then halve, horizontally. If you can see dirt between the layers of your leek, rinse again, then pat dry with a paper towel. Chop garlic clove.
Put potatoes, carrots, leeks, and chopped garlic in a large bowl.
Add 2 tablespoons of olive oil, ¼ teaspoon salt, and ¼ teaspoon pepper. Add bay leaves and thyme sprigs, and stir gently.
In a separate small bowl, stir together butter and piment d’espelette.
Line a large sheet pan with tin foil.
Add chicken breasts to center of the pan, and sprinkle with salt and pepper. Divide spiced butter on top, smearing across the top of each breast.
Add the vegetables around the chicken, in a single layer.
Bake for 25 minutes, and test to see if chicken is done. It should reach 74 degrees Celsius or 165 degrees Fahrenheit on a meat thermometer. If the chicken is done but the vegetables are not yet tender, remove chicken and keep warm on a foil-covered plate.
When both chicken and vegetables are done, you can add more color to them by moving the sheet pan to the top rack and broiling for 2-3 minutes.
Serve chicken and vegetables drizzled with any pan juices. Sprinkle with additional fresh thyme leaves if you’d like.
Notes
The key to this recipe is making sure your vegetable chunks are the right size. You may be tempted to cut your vegetables into larger chunks, but that will not allow them to cook in the same time as the boneless chicken breasts. And leaving your chicken breasts in too long will cause them to dry out. That said, if you choose to use a different cut of chicken such as bone-in chicken thighs, you can cut your vegetables into larger chunks because the chicken thighs will take longer to cook. And, you can always remove the chicken from the sheet pan if it is finished cooking and let the vegetables have extra time in the oven.
Using the broiler at the end of this recipe isn't essential, but it does give you those delicious browned crispy edges on your chicken and vegetables. If you're tempted to roast at a higher temperature to get that browning, I caution you that you may brown the outside of the chicken before the inside is fully cooked. So the broiler is your best option!
Ingredient Tips: If you can't find piment d'Espelette, substitute a mild chili powder or paprika (smoked or regular). Instead of Yukon gold potatoes, you can subsitute red or new potatoes.