Preheat the oven to 350°F and adjust the oven rack to the middle position. Line a 9×13-inch baking pan with parchment paper and set it aside.
In a medium bowl, combine the sliced peaches and sliced strawberries with the filling ingredients. Set the fruit aside while you prepare the cake batter.
In a large bowl, beat the sugar and eggs for 1 to 2 minutes until the mixture is slightly thickened and lighter in color.
Beat in the melted butter, yogurt, and vanilla extract until smooth.
In a separate medium bowl, whisk together the flour, baking powder, and salt.
Gently fold half of the flour mixture into the wet ingredients with half of the milk. Repeat with the remaining flour mixture and milk, mixing only until the batter is smooth.
Scrape the batter into the prepared 9×13-inch pan and smooth the top evenly.
Spoon the strawberry peach mixture evenly over the batter from edge to edge.
In a small bowl, combine the streusel flour, sugar, and softened butter until crumbly.
Sprinkle the streusel evenly over the strawberry peach filling.
Bake at 350°F for 40 to 45 minutes, until the streusel is golden and a toothpick inserted near the center comes out clean.
Cool the buckle completely on a wire cooling rack before slicing into squares and serving.
