Preheat the oven to 400°F (200°C).
In a small bowl, whisk together peach preserves, Dijon mustard, apple cider vinegar, garlic powder, smoked paprika, salt, and black pepper until smooth. Set aside the peach glaze.
Place the halved baby potatoes on a baking sheet. Drizzle with 1 tablespoon olive oil and sprinkle with dried thyme and a pinch of salt. Toss to coat evenly.
Roast the potatoes in the preheated oven for 25-30 minutes, turning halfway through, until golden and tender.
While the potatoes roast, heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Pat the chicken breasts dry with paper towels. Place them in the hot skillet and sear for 4-5 minutes on each side until golden brown but not fully cooked through.
Reduce the heat to medium-low. Brush each chicken breast generously with the peach glaze.
Cover the skillet with a lid and cook for an additional 5-7 minutes, basting with more glaze halfway through, until the chicken reaches an internal temperature of 165°F (74°C).
While the chicken finishes cooking, heat a medium skillet over medium heat. Add the butter and minced garlic and sauté for 1 minute until fragrant.
Add the trimmed green beans to the skillet, season with a pinch of salt and pepper, and sauté for 5-7 minutes until tender-crisp.
Remove the chicken from the skillet and let rest for 3 minutes.
Serve the peach glazed chicken breasts alongside the roasted baby potatoes and sautéed green beans.