1. Preheat the oven to 400F. Melt the butter in a large skillet over medium heat. Add the garlic and cook 30 seconds. Add the spinach and salt; cook, covered, for 2 to 3 minutes. Drain well.
2. Place the chicken breasts between sheets of plastic wrap and pound with a meat mallet to about 8 inches in diameter. Combine the Parmesan and basil; sprinkle 1 tablespoon of the mixture over the chicken breasts. Divide the spinach mixture into 4 portions and place a portion atop each breast. Fold 2 sides of each breast over the filling and roll up tightly. Coat the rolls with the remaining Parmesan mixture.
3. Place the pastry sheets on a lightly floured board. Cut each sheet in half to create six 10x5-inch sheets. Place 1 chicken roll near the end of one sheet; fold the pastry over the ends and roll to enclose. Trim off any excess pastry; press the edges to seal. Place seam side down on an ungreased jelly-roll pan. Repeat with the remaining chicken and puff pastry.
4. Brush the rolls with the egg white and sprinkle with the sesame seeds. Make 2 or 3 cuts on the top of each roll to vent. Bake for about 35 minutes, until the pastry is golden brown and the chicken is cooked through (use a knife to make a small cut on the bottom of one roll, through the pastry and into the chicken, to check).
Tip: Thawing the Puff Pastry
Transfer the puff pastry to the refrigerator several hours before you need it so that has time to thaw evenly without becoming too warm.
Tip: Red Pepper Sauce
Serve the Wellingtons with this super-easy, flavorful sauce: Drain 1 jar (7 ounces) roasted red peppers. In a blender puree the peppers with 1/4 cup olive oil, 1 tablespoon white balsamic vinegar, and 1 minced garlic clove. For a professional presentation, spoon the sauce onto a plate and top with a chicken roll.