Preheat oven to 350°. Place graham crackers in a large resealable plastic bag and using a wine bottle or rolling pin, crush into fine crumbs (some larger crumbs are okay).
Mix 1 cup of graham crumbs with salt, flour, and 2 tbsp. sugar in a medium bowl. Mix with a fork to combine, then add 1 egg and 6 Tbsp. melted butter. Mix with fork until dough forms, then knead with your hands until dough is smooth.
Lightly flour a piece of parchment paper and place dough on top. Lightly flour top of dough, then cover with another piece of parchment. Roll dough into a round (it doesn’t have to be perfect!) about 12" in diameter and ⅛" thick. Periodically peel back parchment and dust with more flour to prevent sticking. Slide entire sheet of parchment paper onto a rimmed baking sheet.
Sprinkle 1 Tbsp. sugar over surface of dough, leaving about a 2" border. Pile fruit onto center of dough and arrange in an even layer, leaving the border.
Sprinkle strawberries with 1 teaspoon sugar and drizzle with remaining melted butter (2 tablespoons).
Using a microplane or fine grater, grate zest of about one-half of lime over fruit. Squeeze lime juice over fruit.
Beat remaining egg in a small bowl and brush egg wash around border of pastry.
Lifting the edges of parchment, fold the border of dough up and over fruit, working your way around in roughly 2" sections, overlapping folds as needed. Press all the way around to secure folds and keep dough in place. It might crack or tear in places, NBD, just pinch it back together.
Brush top of the border with remaining egg wash and sprinkle with remaining sugar. Bake galette until crust is browned around the edges, about 45 minutes. Let cool at least 20 minutes (if you can).
Serve with more lime zest and/or whipped cream and enjoy!