Preheat the oven to 350°F (175°C) and line a large baking sheet with parchment paper. Peel and core the apple, then cut it into small, ¼-inch (6 mm) dice. Set aside.
Combine the dry ingredients. In a medium bowl, whisk together the flour, baking powder, salt and cinnamon.
Cream the butter and sugar. Place the softened butter and sugar in a large mixing bowl. Using a hand mixer, beat on medium speed for about 2–3 minutes, until creamy and slightly lighter in color.
Add the egg, vanilla and finely grated lemon zest. Beat just until smooth and combined.
Add the dry ingredients: add the flour mixture in two additions, mixing on low speed just until the dough begins to come together. Avoid overmixing.
Fold in the apple. Switch to a spatula and gently fold in the diced apple until evenly distributed throughout the dough.
Shape and bake. Scoop about 1½ tablespoons of dough per cookie onto the prepared baking sheet, leaving about 2 inches between them. Keep their shape slightly irregular and rustic.
Bake for 15–18 minutes, until the cookies are set and lightly golden around the edges and underneath.
Cool on the baking sheet for 5 minutes before transferring to a wire rack. Once completely cool, finish with a light dusting of powdered sugar.