Pat 4 boneless, skinless chicken breasts dry with paper towels. Season both sides generously with 1 teaspoon salt and 1/2 teaspoon black pepper. Let sit at room temperature for 5 minutes so seasoning adheres.
Pour 2 tablespoons olive oil into a large skillet (12 inches or wider). Heat over medium-high heat for 2-3 minutes until the oil shimmers and moves freely across the pan. A drop of water should sizzle immediately.
Carefully place chicken breasts into the hot skillet, laying them away from you to avoid splashing. Do not move them for 5-6 minutes. The bottom should be golden brown and release easily when you lift with tongs.
Flip each chicken breast and cook the other side for 5-6 minutes until golden brown. A meat thermometer inserted into the thickest part should read 155°F (this will finish cooking in the sauce). Transfer chicken to a clean plate.
In the same skillet, add 1 medium onion, diced into 1/4-inch pieces. Stir constantly for 3-4 minutes until the onion is soft and translucent. You should smell the sweet onion aroma.
Add 3 cloves garlic, minced very fine. Stir for exactly 1 minute until fragrant. Do not let garlic brown or it will taste bitter.
Sprinkle 1 teaspoon ground ginger, 1/2 teaspoon ground cumin, and 1/4 teaspoon cayenne pepper over the onion and garlic. Stir constantly for 30 seconds. The spices will bloom and smell warm and toasty.
Pour 1 cup chicken broth into the skillet and scrape the bottom with a wooden spoon to release any browned bits (this is called deglazing). Stir in 1/2 cup apricot preserves, 2 tablespoons soy sauce, and 1 tablespoon balsamic vinegar. Mix until the preserves dissolve completely (about 1-2 minutes of stirring).
Stir in 1 cup chopped dried apricots. The sauce should look golden and smell sweet and savory.
Nestle the seared chicken breasts back into the skillet, skin-side up, making sure they are mostly covered by sauce. Reduce heat to medium-low. Cover with a lid (or foil if you don't have a lid).
Simmer for 15-18 minutes. After 15 minutes, insert a meat thermometer into the thickest part of the chicken (not touching bone). It should read 165°F. If not, cover and cook 2-3 more minutes, then check again. The chicken should feel firm to the touch and juices should run clear.
Mix 1 tablespoon cornstarch with 2 tablespoons water in a small bowl until smooth with no lumps. Remove the skillet from the lid. Stir the cornstarch slurry into the sauce.
Simmer uncovered for 2-3 minutes, stirring occasionally, until the sauce thickens enough to coat the back of a spoon. If you run your finger across the spoon, the line should hold.
Taste the sauce. Add more salt, pepper, or soy sauce to your preference. The sauce should taste balanced between sweet (apricot), savory (soy and spices), and tangy (vinegar).
Remove from heat. Sprinkle 2 tablespoons fresh cilantro, finely chopped, over the chicken and sauce.
Let rest in the pan for 2-3 minutes before serving. The residual heat will continue to cook any remaining undercooked portions and the sauce will set slightly.
Checkpoint: You are ready to serve when the chicken reaches 165°F internally, the sauce coats a spoon, and the apricots are tender and infused with sauce.