Adjust rack to top position and preheat oven to 450 degrees. Wash and dry all produce. Dice potatoes into 1/2-inch pieces. Toss on a baking sheet with large drizzle of olive oil, salt, and pepper. Roast on top rack until browned and tender, 20-25 minutes.

Meanwhile, halve, peel, and thinly slice shallot. Halve lemon. In a small bowl, combine jam, stock concentrate, half the chili powder, and 1/4 cup water (1/3 cup for 4 servings).

In a second small bowl, combine shallot, juice from lemon halves, 1/2 tsp sugar (1 tsp for 4 servings), and a pinch of salt. Set aside, stirring occasionally, until ready to serve.

Pat chicken dry with paper towels; season all over with salt and pepper. Heat a large drizzle of olive oil in a large pan over medium-high heat. Add chicken and cook until browned and cooked through, 5-7 minutes per side. Transfer to a plate. Add jam mixture to pan and cook until slightly thickened, 2-3 minutes. Remove from heat; stir in 1 TBSP butter (2 TBSP for 4 servings) until melted. Season with salt and pepper.

In a large bowl, toss together mixed greens, pickled shallot (and pickling liquid), a large drizzle of olive oil, and a pinch of salt and pepper.

Divide potatoes, chicken, and salad between plates. Top chicken with sauce and serve.