Heat the oven to 175 C / 350 F. Grease a 9-inch round cake pan and line the bottom with parchment paper.

Melt the butter in a light-colored saucepan over medium heat, stirring occasionally, until the foam settles and the milk solids at the bottom turn amber and smell like toasted nuts, about 5 to 6 minutes.

Pour the browned butter immediately into a large mixing bowl and let it cool for 5 minutes.

Whisk the brown sugar into the cooled butter until combined.

Add the eggs one at a time, whisking well after each addition until the mixture looks smooth and slightly thickened.

Whisk in the sour cream and vanilla extract until fully incorporated.

Add the flour, baking powder, cinnamon, cardamom, and salt. Fold with a spatula until just combined and no dry streaks remain, do not overmix.

Fold in the diced pears gently, reserving a small handful for the top.

Scrape the batter into the prepared pan and spread evenly.

Scatter the reserved pear pieces across the top, then mix the 1 tbsp brown sugar with the 0.25 tsp cinnamon and sprinkle over the surface.

Bake for 33 to 36 minutes, until the top is deep golden and a skewer inserted into the center comes out with just a few moist crumbs.

Cool in the pan for 10 minutes, then run a knife around the edge, unmold onto a wire rack, and cool for at least 15 minutes before slicing.