Mash 3 cups sliced strawberries with 1 cup sugar in a saucepan over medium heat.
Bring mashed strawberry mixture to a boil, stirring frequently.
Mix cornstarch with water in a small bowl and pour into mashed strawberries; reduce heat to medium-low.
Bring strawberry mixture back to a simmer, stirring constantly, until thickened, about 10 minutes. Set aside.
Bring half-and-half to a boil in a saucepan; remove from heat.
Beat egg and egg yolk with an electric mixer in a bowl until frothy; gradually mix in 3/4 cup of sugar, then beat until the egg mixture is thick, pale yellow, and forms a ribbon when beater is lifted out of the bowl, about 3 minutes.
Beat in flour until smooth.
Very slowly pour hot half-and-half into the egg mixture in a thin stream of droplets, beating continuously.
Transfer the mixture to a saucepan and place over medium heat. Cook, stirring constantly, until the custard thickens. Reduce heat to medium-low; continue cooking while stirring with a wooden spoon until flour is cooked, 2 to 3 more minutes.
Remove custard from heat, and stir in butter and vanilla extract until well combined.
Spread custard in an even layer over the bottom of graham cracker crust.
Pour mashed strawberry mixture over 2 cups of sliced strawberries in a bowl; stir to combine. Top the custard with the strawberry mixture.