1. Season chicken all over with salt and pepper. Melt butter with the oil in a large enameled cast-iron Dutch oven over medium-high heat until just bubbling. Add half the chicken pieces, skin sides down; cook, turning once, until golden, 2 to 3 minutes per side. Transfer chicken pieces to a plate; set aside. Repeat with remaining chicken pieces; add to plate. Remove pot from heat; let cool slightly.

2. Return pot to medium-low heat, and add leeks. Cook, stirring frequently, until leeks begin to soften and are pale golden, about 3 minutes. Add hard cider and thyme. Move leeks to edges of pot, and add all the chicken pieces to pot, skin sides down. Arrange leeks over chicken. Cover, and cook 15 minutes (if liquid is bubbling rapidly, reduce heat to low). Turn chicken pieces, and cook until breasts are cooked through, about 5 minutes more. Use a slotted spoon to transfer chicken breasts to a plate, and cover to keep warm. Adjust leeks so they are submerged in liquid. Cook, uncovered, until the remaining chicken pieces are tender and cooked through, about 10 minutes.

3. Transfer all of the chicken to a warm serving platter. Remove leeks from pot, and arrange them around the chicken. Cover to keep warm. Return pot to medium heat. Cook, uncovered, until liquid has reduced by about half (to a scant 2/3 cup), 8 to 10 minutes.

4. Reduce heat to medium-low. Whisk in the creme fraiche and parsley. Ladle pan sauce over chicken and leeks. Serve immediately.