Preheat the oven to 350 degrees F.
Season both sides of the chicken with salt and pepper, to taste. In an oven-proof saute pan, heat 1 tablespoon olive oil and sear the chicken, skin side down, until the skin is crisp and golden brown, about 5 minutes. Flip the chicken over and put the pan in the oven until the internal temperature reaches 165 degrees F on an instant-read thermometer, about 15 minutes. Remove to a plate and keep warm.
Meanwhile, liberally salt a large pot of water and add the potatoes. Bring the water to a boil over medium heat and cook the potatoes they are fork tender, about 20 minutes. Drain the potatoes in a colander and spread them out a sheet pan. Drizzle with remaining 2 tablespoons olive oil, and sprinkle with salt and pepper, to taste. Bake in the oven until golden brown.
Beurre Blanc: Cut off the tops of the jalapenos. Toss them in a small bowl with the olive oil and transfer them to a small sheet pan. Roast until the skin starts to darken and blister, about 15 minutes. Remove the pan from the oven and let the peppers cool a bit. Pull off the skin then cut them in half, lengthwise, and remove the seeds. Dice the jalapenos and set aside.
In a sauce pot over medium heat, stir together the vinegar, white wine, garlic and thyme. Let simmer until the liquid is reduced and there is only a tablespoon of liquid left in the pot. Discard the garlic clove and thyme sprigs. Add the jalapenos to the reduction. Turn down Reduce the heat to low, then whisk in the butter, little by little, until blended and smooth. Season with salt and pepper, to taste. Keep warm and set aside.
Pepper puree: Roast and peel the red pepper using the same method as the jalapenos. (To save time, roast both jalapeno and red peppers at the same time.) In a saute pan, over medium heat, add the olive oil and the onions. Saute until they become soft, around 3 minutes. Stir in the poblano peppers and cook for 2 minutes. Turn off the heat. In a blender or food processor, puree the roasted red peppers, the onion mixture, and chicken stock until smooth. Season with salt and pepper, to taste.
Spoon some of the pepper puree onto each serving plate and arrange a chicken breast on top. Drizzle with the beurre blanc and serve the potatoes on the side.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.