Preheat your oven to 350°F (175°C) and prepare a 9x9-inch baking pan by lining it with parchment paper.

In a medium bowl, whisk together the all-purpose flour, granulated sugar, light brown sugar, and a pinch of salt until well combined.

Pour in the melted butter, stirring until the mixture forms large, crumbly clumps. Set aside.

In a large bowl, combine the browned butter, granulated sugar, light brown sugar, and vanilla extract, whisking until pale and creamy.

Add the eggs one at a time, mixing well after each addition. Incorporate the full-fat yogurt until combined.

In another bowl, sift together the all-purpose flour, baking powder, and remaining salt. Gradually fold this into the wet mixture.

Pour the batter into the prepared pan, smoothing it evenly with a spatula.

Toss the chopped peaches with a bit of flour and brown sugar to coat. Layer the peaches over the batter evenly.

Sprinkle the crumb topping generously over the peaches, ensuring the fruit is covered while leaving some gaps.

Bake for 40-50 minutes, or until golden brown and a toothpick inserted in the center comes out clean.

Let the cake cool in the pan for at least 30 minutes before lifting out, slicing, and serving.