With a stand mixer fitted with the paddle attachment, or a handheld mixer and a large mixing bowl, whip the butter, sugar, and salt on high speed until light and creamy, about 2 minutes.
Incorporate the egg, vanilla extract, and almond extract. Blend on medium speed until fully combined, scraping down the bowl's sides as necessary.
Reduce the mixer to low and add the flour in increments. Blend just until no flour streaks remain, taking care not to overmix. At this stage the dough might look crumbly, which is fine.
Gently knead the dough until it becomes smooth. Split into 2 equal portions and form each into a flat disk. Proceed to the next step, or wrap each disk in plastic wrap and refrigerate until baking time.
Set the oven to 350°F (180°C / gas mark 4). Prepare baking sheets by lining them with parchment paper or non-stick baking mats.
Sprinkle flour over your work surface and rolling pin. Roll out one dough disk at a time to 1/4 inch (6 mm) thickness, working from the center outward and rotating the dough occasionally to avoid sticking.
With cookie cutters, press out shapes, pushing the cutter fully down to get clean edges. Move the cut shapes onto the lined baking sheets.
Do the same with the remaining dough and re-roll the scraps. If the dough gets too warm, place it in the refrigerator to chill.
Bake the cookies for 8 to 10 minutes, until the edges begin to turn lightly golden.
Take the cookies out of the oven and allow them to cool on the baking sheet for 5 minutes. Then move them to a wire rack to cool completely.