In a large bowl, beat together the butter and sugar until smooth. You can do this using a hand mixer, or with a stand mixer if you have one. Add in the eggs and vanilla and continue beating until light and fluffy. In all, this should take about 3-4 minutes.
In a separate medium sized bowl, stir together the flour, salt, baking soda, and baking powder.
Add the dry ingredients to the bowl with the wet ingredients and beat with the mixer until well combined. The dough should start to stick together.
Line a baking sheet with parchment paper and set aside. Be sure to have an open surface available for rolling out the dough. Sprinkle the surface with flour.
Roll the cookie dough out on the prepared surface to 3/8 inch (9.5mm) thickness. Use cookie cutters to cut shapes from the dough in circles, squares, and hearts. Carefully place each cut out cookie onto the parchment lined baking sheet.
Place the tray of cookies into the freezer for 20 minutes to firm up the dough. Preheat the oven to 350°F/177°C.
Line a second baking tray with parchment paper. Transfer some of the frozen cookies to this sheet, leaving 2 inches in between them. Bake the cookies, one tray at a time, in a preheated oven for 15-17 minutes, or until the edges are just slightly brown.
Allow cookies to cool for 5 minutes on the baking tray, then transfer them to a wire rack to cool completely before frosting.
Buttercream
In a large bowl, beat together butter, confectioner's sugar, and vanilla until light and fluffy.
Separate the icing into four bowls. Leave one white, and add food coloring to the others to get your desired shades of pink, black, and tan. Transfer the frosting to piping bags (no icing tips needed!) and tie or clip the ends of the bags.
Use scissors to cut small openings into the tips of each icing bag. For the background colors you can cut larger holes than the detail colors.
Start by filling in the backgrounds of each cookie using your desired icing colors. You can leave the icing with ridges, or use a small spatula to smooth the icing out. Continue decorating the cookies to resemble cat faces, hearts, and sentiments.
Notes
To Store: These Valentine cookies can be stored at room temperature in an airtight container for up to three days, or in the fridge for up to one week. Store cookies in a single layer to avoid them sticking together.
Be sure to freeze the cookies after cutting out shapes. This keeps them from spreading during baking.
If the dough seems too sticky, add more flour while rolling.
This recipe makes thick cutout cookies. You can make more cookies if you make them thinner, but they will need less time in the oven.