Place 2/3 cup of the all-purpose flour, the whole wheat flour, mesquite flour, salt and sugar into a food processor, and pulse several times to combine. Add butter evenly over the dry ingredients, and pulse until the dough collects in clumps, about 25–40 short pulses. Use a spatula to spread the dough evenly around the bowl of food processor.
Sprinkle in the remaining cup of all-purpose flour, and pulse until dough is barely broken up, about 5 short pulses.
Transfer to a large bowl. Sprinkle with cold water, fold and press with a rubber spatula until it comes together into a ball.
Divide the dough into 2 equal portions. Form each portion into a 4-inch disk. Wrap in plastic, and refrigerate for 2 hours. Roll each disk into a 12–13-inch round.
Place in a 9–10-inch pie tin, and cut a 1-inch overhang with scissors. Fold the overhang underneath to form a rolled edge, and crimp as desired. Refrigerate for at least an hour before proceeding.
I recommend blind baking the crust so it holds up to the filling. Line the crust with a sheet of foil large enough to form a skirt over the edges to prevent burning. Weigh down the foil with pie weights or salt or sugar filled to the brim and packed against the crust. Preheat oven to 350°, and blind bake the crust for 1 hour.
Carefully remove the foil and weights, and let the crust cool before proceeding.