To rub the chicken, add all of the ingredients for the chicken (paprika, garlic powder, oregano, thyme, cayenne, salt, pepper, water, oil) into a glass container or plastic storage bag. Mix to combine into a thick paste. Add the chicken and rub the paste all around. Set aside.
Cut off the stem end of the Brussels sprouts and then slice in half. Slice the olives in halves or thirds. The butternut squash pieces should be no larger than ½ inch by ½ inch so trim them down as needed. Slice the Olives (I like 3 slices per olive).
To a large sheet pan, add the Brussels sprouts on one side and the cut butternut squash to the other side. Drizzle the olive oil over the veggies and then sprinkle with the salt, paprika, and garlic powder. Rub the oil and seasonings all of the veggies with hands, keeping the 2 veggies separate. Add the chicken thighs onto the pan in the center between the Brussels and squash. Sprinkle the olives over the chicken and the Brussels sprouts (not over the squash).
Roast in the oven for 20 minutes, just until the squash is fork tender. When the squash is soft, transfer it to a food processor. Put the chicken and Brussels back in the oven for a final 5 minutes.
Blend until a smooth mash. If you need to add a tablespoon of water to help it along, do so.