Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Mix together the spices in a shallow bowl. Dredge the top of each piece of chicken in the spices until coated.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Place the chicken spice/skin side down in the pan, sprinkle with any remaining spices that didn't stick to the chicken, and sear until golden brown, 3 to 4 minutes. Turn over and sear the bottom of the pieces for another 2 to 3 minutes until brown. Transfer to the center of the baking sheet, turn off the heat, and reserve the remaining oil in the pan.
Nestle the cubed squash, sliced sprouts, and garlic cloves around the chicken on the baking sheet. Drizzle the cooking oil over veggies and toss to coat. Bake until chicken is cooked all the way through (no longer pink in the middle) and the veggies can easily be pierced with a fork, about 25 minutes.
Wipe out the skillet and melt the butter over medium heat. Add the sage leaves to the pan and cook while stirring until they just begin to darken in color and become crispy, and the butter browns. Immediately remove from heat. This sauce can overcook easily so sometimes I even immediately remove it from the pan so it doesn't keep cooking.
Remove baking sheet from oven, pour brown butter sage over veggies, and serve.