Step 1: Prepare the Dough

1. Mix Dry Ingredients: In a medium mixing bowl, whisk together the flour, baking powder, and salt. Set aside.
2. Cream Butter and Sugar: In a large mixing bowl, using an electric mixer, beat the softened butter and granulated sugar together until light and fluffy, about 3-4 minutes. This step is essential for creating a tender, airy texture.
3. Add Eggs and Vanilla: Beat in the eggs, one at a time, ensuring each is fully incorporated before adding the next. Stir in the vanilla extract (and lemon zest or almond extract, if using) until well combined.
4. Combine Wet and Dry Ingredients: Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Be careful not to overmix, as this can lead to dense cookies.

Step 2: Chill the Dough

1. Shape the Dough: Form the dough into a disc, wrap it in plastic wrap, and refrigerate for at least 1 hour. Chilling the dough makes it easier to handle and helps prevent the cookies from spreading too much during baking.

Step 3: Roll Out and Cut the Dough

1. Preheat Oven: Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or silicone baking mats.
2. Roll Out the Dough: On a lightly floured surface, roll out the chilled dough to about ¼-inch thickness. Use a cookie cutter or a round cutter to cut out shapes, and place them on the prepared baking sheets, spacing them about 1 inch apart.

Step 4: Bake the Tea Cakes

1. Bake the Cookies: Bake the tea cakes in the preheated oven for 10-12 minutes, or until the edges are lightly golden. The centers should still look slightly soft, as they will firm up as they cool.
2. Cool the Cookies: Remove the baking sheets from the oven and let the tea cakes cool on the sheets for 5 minutes before transferring them to a wire rack to cool completely.

Step 5: Serve and Enjoy

1. Serve: Once cooled, serve the tea cakes plain or dusted with powdered sugar. Enjoy them with a cup of tea, coffee, or a glass of milk for a delightful treat.