Prepare Your Workspace: Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper and set aside. Keep raspberries in the freezer until ready to use.
Infuse the Sugar: In a large mixing bowl, combine the granulated sugar and freshly grated lemon zest. Using your fingertips, massage the zest into the sugar for about 30 seconds. This releases the essential oils from the zest, creating a more aromatic and flavorful base for your cookies.
Create the Cookie Base: Add the softened butter and brown sugar to the lemon-infused sugar. Beat with an electric mixer on medium-high speed for 3-4 minutes until the mixture becomes light, fluffy, and noticeably paler in color. Add the egg yolk, lemon juice, and vanilla extract, then mix until thoroughly combined and smooth.
Incorporate Dry Ingredients: In a separate bowl, whisk together the flour, salt, baking powder, and baking soda. Gradually add this dry mixture to the wet ingredients, mixing on low speed just until combined. Stop mixing when you still see a few streaks of flour remaining in the dough to avoid overmixing.
Add Raspberries: Remove the frozen raspberries from the freezer and quickly chop them into smaller pieces. Using a rubber spatula, gently fold the raspberry pieces into the cookie dough with just a few strokes. The goal is to incorporate them without overmixing, which would cause the raspberry juice to bleed throughout the dough and turn it pink.
Form the Cookies: Using a 3-tablespoon cookie scoop or measuring spoon, portion the dough into balls (approximately 2 inches in diameter). Place 5 dough balls on each prepared baking sheet, leaving ample space between them for spreading. If desired, sprinkle the tops lightly with flaky sea salt to enhance the flavor contrast.
Bake to Perfection: Bake the cookies for 12-15 minutes, rotating the pans halfway through baking time. Look for a light golden brown color around the edges while the centers remain slightly soft. Remove from the oven and allow the cookies to rest on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.