Heat a large saucepan over medium-high heat. Add 1 tablespoon water and spinach; cover and cook 5 minutes or until spinach wilts, stirring occasionally. Place spinach mixture in a colander, pressing until barely moist.
Heat 1 teaspoon of oil in a small saucepan over medium-high heat. Add 2 tablespoons chopped shallots, 2 tablespoons water, and garlic; cover and cook 3 minutes or until moisture evaporates. Spoon shallot mixture into a medium bowl. Add the spinach, feta, breadcrumbs, oregano, 1/4 teaspoon salt, 1/8 teaspoon pepper, and egg white.
Cut horizontally through center of breast, cutting to, but not through, other side using a sharp knife; open flat as you would a book. Place breast between 2 sheets of plastic wrap; pound to an even 1/2-inch thickness using a meat mallet or rolling pin. Discard plastic wrap. Spread spinach mixture over turkey, leaving a 1-inch border. Roll up breast, jelly-roll fashion, starting with one short side. Secure at 2-inch intervals with twine. Rub 1/2 teaspoon salt and 1/4 teaspoon pepper evenly over turkey.
Preheat oven to 325°.
Heat 2 teaspoons oil in a large Dutch oven over medium-high heat. Add the turkey; cook 5 minutes, browning on all sides. Remove turkey from pan. Add 2 tablespoons shallots to pan; sauté 30 seconds. Stir in wine, scraping pan to loosen browned bits. Add turkey and broth to pan; bring to a boil. Cover and bake at 325° for 40 minutes or until a thermometer inserted in thickest portion of turkey registers 170°. Remove turkey from pan; keep warm.
Place pan on stovetop over high heat. Combine cornstarch and 1 tablespoon water, stirring with a whisk. Add cornstarch mixture to pan; bring to a boil. Cook 1 minute or until slightly thick, stirring constantly. Remove from heat. Add butter, stirring with a whisk. Remove and discard twine from turkey. Cut turkey into 8 slices. Serve sauce with the turkey. Garnish with oregano sprigs, if desired.
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