Preheat your oven to 350°F (175°C). Grease your baking pan with butter or line it with parchment paper for easy removal.
In a medium bowl, whisk together the flour, baking powder, salt, and both sugars until well mixed.
In a separate bowl, whisk the melted butter, egg, vanilla extract, and grated lemon zest until smooth.
Pour the wet ingredients into the dry ingredients and stir gently with a spatula until just combined. Be careful not to overmix to keep your cake tender.
Gently fold the fresh raspberries into the batter, trying not to break them too much to avoid turning the batter pink.
Pour the batter into your prepared pan, smoothing the top. Bake for 30-35 minutes or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes before transferring it to a wire rack. Dust with powdered sugar if desired before slicing and serving.