Turn a gas grill to medium high or light a charcoal fire, letting the coals burn until they are covered with gray ash but still very hot.
Cut the neck off of the butternut leaving the bulbous round end behind (reserve the bulbous end for another use). Peel (a knife is easiest) and slice the butternut neck into ½-inch slabs.
Lightly oil one side of the onion rounds and butternut slabs with a pastry brush or oil mister, then season with salt and pepper. Place the onions and butternut oil-side down on the grill. Oil the other side of each slice and season with a little more salt. Grill until browned and tender (about 5 to 8 minutes per side), turning halfway through. Remove from grill and cool. Chop into small (about ½ inch) pieces and scoop into a bowl.
Place the beans in a small pot or skillet and set over medium heat (or on the grill). Mash as smooth a consistency as you like with the back of a spoon or an old fashioned potato masher. Thin with water or bean broth to an easily spreadable consistency. Taste and season with salt if necessary. Keep warm.
When you are ready to serve, spread a layer of beans on each tostada, top with butternut mixture and sprinkle with queso aňejo. Serve with salsa for each guest to add al gusto.