Preheat the oven to 375 degrees F (190 degrees C). Lightly grease a 8x6-inch pan and line with parchment paper.
Whisk flour, sugar, and 1/4 teaspoon cinnamon together in a large bowl. Cut in butter until the pieces look like small pebbles. Cut in egg with a pastry cutter. Blend dough together with a gentle kneading motion. Set aside 1/2 cup dough for the topping.
Pat remaining dough into the bottom of the prepared pan. Top with strawberry compote.
Add oats and remaining cinnamon to the reserved dough. Pinch off pieces of dough and cover the strawberry compote as much as possible.
Bake in the preheated oven until the top is golden brown and the edges pull away from the sides of the pan, 40 to 45 minutes. Cool completely before serving.