Preheat oven to 375°.
Combine first 7 ingredients in a food processor; process until smooth.
Remove and discard giblets and necks from hens. Rinse hens with cold water; pat dry. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Rub pesto under loosened skin. Gently press skin to secure. Lift wing tips up and over back; tuck under hens.
Place hens on a broiler pan coated with cooking spray. Insert a meat thermometer into meaty part of a thigh, making sure not to touch bone.
Combine potatoes, 1 tablespoon oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper, tossing well to coat. Arrange potatoes around hens; bake at 375° for 45 minutes or until thermometer registers 180° and potatoes are tender.
Remove hens and potatoes from pan, and cover loosely with foil. Let stand 10 minutes. Discard skin. Cut hens in half, and cover loosely with foil.
Place a zip-top plastic bag inside a 2-cup glass measure. Pour pan drippings into bag; let stand 10 minutes (the fat will rise to the top). Seal bag, and carefully snip off 1 bottom corner. Drain drippings into pan, stopping before fat layer reaches opening; discard fat.
Place the pan over medium-high heat. Stir in broth, scraping pan to loosen browned bits. Combine 1 tablespoon water and cornstarch, stirring well with a whisk. Add to pan. Bring to a boil; cook until reduced to 1/2 cup (about 3 minutes). Serve sauce with hens and potatoes. Garnish with basil sprigs, if desired.