Preheat the oven to 350°F and grease a 9-inch round cake pan with butter, then line it with parchment paper, pressing it into the butter to secure. To make the parchment paper easier to handle, crumple it into a ball and run under water, then squeeze and flatten it out and dry it off.
In a medium bowl, whisk together 2 cups all-purpose flour, 2 teaspoons baking powder, and ½ teaspoon salt and set aside.
In a stand mixer bowl fitted with a paddle attachment, mix together ½ cup granulated sugar, ⅓ cup light brown sugar, and 1½ tablespoons lemon zest for 1 minute. This helps infuse the sugar with lemon flavor.
Add the ½ cup salted butter and 1 teaspoon vanilla extract to the bowl with the sugar and beat at medium-high speed for 5 minutes, scraping down the sides of the bowl as needed.
Add 2 large eggs, one at a time, mixing for 30 to 45 seconds after each addition.
Add the dry ingredients, alternating with the ¾ cup buttermilk, at low speed until combined.
Fold in ⅔ of the 10 ounces raspberries with a rubber spatula, then transfer the batter into the prepared cake pan.
Add the remaining raspberries to the top of the cake, gently pressing them into the batter.
In a small prep bowl, rub 3 tablespoons coarse sparkling sugar and ½ tablespoon lemon zest with your fingers to infuse the sugar, then sprinkle it over the top of the cake.
Bake for 45 to 55 minutes until a toothpick comes back clean from the center or a digital kitchen thermometer reads 200°F.
Remove from the oven and let cool in the pan for about 10 minutes before transferring to a wire rack to cook for at least another 20 minutes before slicing with a serrated knife and serving.