Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together flour, baking powder, and salt. Set aside.
In a large bowl, use a wooden spoon or spatula to cream together softened butter, oil, and sugar until light and fluffy, about 2 minutes. The mixture should look pale and slightly fluffy.
Mix in the egg, lemon juice, lemon zest, and vanilla extract. Stir until completely combined and smooth.
Add the dry ingredients to the wet ingredients. Stir gently until just combined. Do not overmix.
Using a medium cookie scoop, about 1.5 tablespoons, drop dough onto the prepared baking sheets, spacing cookies 2 inches apart. Bake for 10–12 minutes, until the edges are just set but the centers still look slightly underdone.
Let cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
While the cookies cool, beat together powdered sugar, cream, butter, lemon extract, vanilla extract, and salt until smooth and spreadable. Add food coloring if desired. If the frosting is too thick, add cream 1 teaspoon at a time. If it is too thin, add more powdered sugar.
Once cookies are completely cool, spread frosting generously on top using a butter knife or offset spatula. Sprinkle with lemon zest or edible glitter if desired.
