Season chicken with 1 ½ teaspoon salt and ½ teaspoon pepper. In a Dutch oven or heavy pot with a lid, heat the oil over medium high heat until hot but not smoking. Add the chicken and sear on each side for about 3 minutes. Transfer to a platter.
Reduce the heat to medium and add 3 tablespoons of butter to the pot and allow it to melt. Add leeks, cover and cook, stirring often until tender. Stir in the flour followed by the cider, broth and minced thyme and bring to a boil. Return the chicken to the pot, cover and reduce the heat to medium-low. Simmer, stirring occasionally for 15 minutes.
Peel and core the apples and cut them into ½ inch thick wedges. Place in a bowl and sprinkle with lemon juice and toss. In a large frying pan and medium high heat, melt 1 tablespoon butter and sauté the apples until the edges are showing a golden color, approximately 4 minutes. Carefully pour in the brandy and reduce the heat to low. Using a long handled match, light the brandy and allow the flame to burn for 30 seconds, then cover to extinguish the flame.
Once the chicken has simmered 15 minutes, stir the apples into the pot with the chicken and continue to cook for an additional 5 minutes. Check the chicken for doneness (no visible pink) and continue cooking until chicken is done. Taste and adjust the seasonings as necessary. Serve the chicken with apples and sauce spooned over each breast and garnish with a thyme sprig.