Mix all but 3 tablespoons of 1 package (7 oz.) pesto with 4 cups (about 1 lb.) shredded, skinned cooked turkey and spoon an equal portion of the mixture on a quarter section of each of 8 packaged crêpes (9-in.). Top turkey mixture on each crêpe with 1 tablespoon shredded jack cheese (you'll need 1 cup total).
Fold crêpes in half over filling, then in half again to make a triangle. Set triangles, 3-layer side down, slightly apart in 2 nonstick or lightly oiled 10- by 15-inch pans.
Bake in a 400º oven until filling is hot in the center and crêpe edges are crisp, about 6 minutes; switch pan positions after 3 minutes. Transfer crêpes to plates. Dot crêpes with remaining pesto.