Preheat oven to 375°F. Line two baking sheets with parchment paper.
In a small bowl, stir together the strawberries, lemon juice, and 2 tablespoons of the sugar; set aside.
In a large bowl, whisk together the lemon zest and remaining sugar. Rub the zest into the sugar with your fingertips until moist and fragrant.
Add the flour, baking powder, and salt to the zest/sugar mixture and whisk to combine. Using a pastry cutter to cut the butter into the flour mixture until you have coarse crumbs. Add the cream to the bowl and stir until the dough starts to come together, then gently fold in the strawberry mixture.
Use a small cookie scoop (about 1 1/2 tablespoons) to drop dough onto the prepared baking sheet, evenly spaced apart. Sprinkle with coarse sugar. Bake for about 10-15 minutes, or until the cookies are golden brown. Transfer the pans to wire racks and let the cookies cool. The cookies are best the day they're made, but can be kept in an airtight container for 1 day.