Preheat oven to 400F. Season chicken on both sides with salt and pepper to taste. Heat butter and vegetable oil in a large skillet over medium-high heat until melted and hot.
Place chicken thighs skin-side down in pan and sear 2-3 minutes on both sides until golden brown. Remove chicken from skillet and transfer to a plate.
Drain grease from skillet and wipe clean. Heat sesame oil in skillet over medium-high heat until shimmery. Add garlic and ginger and saute 1 minute until fragrant. Add honey, soy sauce, and rice vinegar to pan and bring to a simmer, then reduce heat to medium-low and let simmer 5 minutes until slightly thickened. Stir in sesame seeds.
Toss about half of honey sesame sauce with acorn squash and kale in a large bowl. Arrange acorn squash and kale in a greased 9x13 baking dish. Arrange chicken on and around squash and kale. Spoon remaining sauce over top of chicken.
Bake chicken at 400F 25-30 minutes or until chicken registers 165F, acorn squash is tender, and kale is crispy. (cover chicken loosely with tin foil if it starts to brown too quickly)
Use a spoon to drizzle sauce drippings in pan over chicken and squash. Sprinkle green onions on top. Serve warm and enjoy!