A brushpile is, basically, just a pile of woody branches. Ideally, the first foot or so should be made of woody branches 3 to 6” in diameter, criss-crossed to leave lots of empty spaces inside. Above this, pile branches randomly, leaving plenty of nooks and crannies for birds to find. It attracts the most birds when you exclude small stuff like leaves and grass clippings.
Avoid cleaning your yard fastidiously. Insect-eating birds love to pick through the leaf-litter on the ground, in search of small spiders and other edibles. If your yard is all lawn - completely free of things like tall grass and leaf-litter, birds won't hang around. You may not want to leave your entire yard "natural", but maybe an unused corner can be left for insect eating birds.
Please - do what you can to appeal to all the birds that don't care what's in your birdfeeder.