Preheat oven to 325°F. Lightly coat a 9-inch springform pan with cooking spray. Wrap outside of pan with heavy-duty aluminum foil. Stir together graham cracker crumbs, melted butter, and 2 tablespoons of the sugar in a medium bowl. Press mixture on bottom and 1 inch up sides of prepared pan. Bake in preheated oven until set, 7 to 8 minutes. Transfer to a wire rack; cool completely, about 30 minutes.
Meanwhile, process chopped strawberries in a food processor until completely smooth, about 1 minute, stopping to scrape down sides as needed.
Beat cream cheese with a stand mixer fitted with a paddle attachment on medium speed until creamy, 1 to 2 minutes. Gradually add flour and remaining 1 1/4 cups sugar, beating until smooth, about 1 minute. Add whole eggs, 1 at a time, beating on low speed just until blended after each addition (do not overbeat). Add egg yolk, and beat just until incorporated. Beat in zest, strawberry puree, and 2 teaspoons vanilla on low speed just until combined. Gently stir in food coloring gel until desired shade is reached. Pour batter into prepared pan, and place on a large rimmed baking sheet.
Bake in preheated oven just until center is set, 1 hour and 10 minutes to 1 hour and 20 minutes. Turn oven off, and let cheesecake stand in oven, with door closed, 15 minutes. Remove cheesecake from oven, and gently run a knife around outer edge of cheesecake to loosen from sides of pan. (Do not remove sides of pan.) Cool completely in pan on a wire rack, about 2 hours. Cover and chill 8 to 24 hours.