Preheat oven to 400 degrees, spray or brush the bottom of a sheet pan with olive oil and set aside.
Wash the potatoes and cut into halves (for smaller baby potatoes), or quarters (for larger baby potatoes). Put in a large bowl.
Wash the asparagus and trim the fibrous ends, then cut into 1 to 2-inch pieces and add to the bowl with the potatoes.
Add the olive oil, pressed or minced garlic cloves, salt, and pepper to the potatoes and asparagus, and mix together until thoroughly coated. Set aside.
Mix together the ingredients for the smokey barbecue spice blend, and sprinkle generously over each side of the trimmed chicken thighs.
Set the chicken evenly onto the prepared sheet pan, not on top of the potatoes and asparagus, but moving aside the potatoes to set the chicken directly on the sheet pan. We've found that if you put the chicken on top of the potatoes, the potatoes underneath won't cook well and will still be hard.
Bake in the pre-heated oven for about 20 minutes. Brush a little olive oil on top of the chicken, then turn on your broiler to high, adjust the oven rack to 4-5 inches away from the broiler, and broil the chicken for 3-4 minutes, keeping an eye on the chicken to make sure it doesn't over-brown or burn.
Remove from the oven and let rest for 5-10 minutes before serving.
Don't set the chicken on top of potatoes, or the potatoes won't cook fully and will be hard.