Chicken and Mushroom Quesadillas with Carrot and Mango Slaw

Preheat oven to 425°F. Stir cumin, 3 Tbsp. oil, 1 tsp. salt, and 1/2 tsp. pepper in a large bowl. Add chicken and mushrooms and toss to coat. Spread on a rimmed baking sheet and roast until an instant-read thermometer inserted into thickest part of thigh registers 165°F, 15–17 minutes.

Meanwhile, juice limes to yield 6 Tbsp. juice. Blend yogurt, 3 Tbsp. lime juice, and 3 Tbsp. cilantro in a blender until smooth.

Shave carrots with a vegetable peeler lengthwise into ribbons (or use the large holes of a box grater). Whisk 1 Tbsp. oil and remaining 3 Tbsp. lime juice, 1/4 tsp. salt, and 1/4 tsp. pepper in a large bowl. Add carrots and mango; toss gently to coat.

Remove baking sheet from oven, arrange spinach over chicken, and continue to roast until spinach is wilted, about 2 minutes. Transfer chicken to a cutting board, leaving spinach on sheet, and thinly slice.

Arrange tortillas on a work surface. Dividing evenly, layer cheese, chicken, mushrooms, and spinach on one side of each tortilla. Fold tortillas in half to create half-moons.

Heat 1 1/2 tsp. oil in a large heavy skillet over medium-low until hot. Cook 2 quesadillas, turning once, until cheese is melted and tortillas are browned, 1–2 minutes per side. Transfer quesadillas to serving plates, then cook remaining quesadillas with remaining 1 1/2 tsp. oil.

Sprinkle quesadillas with cilantro leaves and serve with yogurt sauce and carrot-mango slaw alongside.

Chicken and mushrooms can be cooked and yogurt sauce can be made 4 days ahead; cover and chill.