Begin by placing softened butter and sugar into a mixing bowl. Use a hand mixer to blend until the mixture becomes fluffy.
Next, incorporate vegetable oil, egg, heavy cream, and vanilla into the mixture. Blend until the mixture turns creamy.
Sift in cake flour, cream of tartar, baking powder, and salt into the bowl. Gently fold all the ingredients together until a thick dough forms. Cover the dough with plastic wrap and refrigerate it for 1 hour.
Preheat your oven to 350 degrees Fahrenheit and line a baking sheet with parchment paper.
Use a 2-inch cookie scoop to portion out the chilled cookie dough onto the prepared baking sheet, leaving about 2 inches of space between each dough ball.
Bake for approximately 12 minutes, or until the edges of the cookies are barely browned and the cookies are set.
While the cookies are baking, prepare the frosting. In another mixing bowl, blend softened butter with a hand mixer until it becomes fluffy and the color pales.
Add powdered sugar and salt to the bowl, then blend until fully incorporated. The frosting may still appear crumbly at this stage.
Incorporate vanilla and heavy cream into the frosting mixture, blending until it reaches a creamy consistency. Optionally, add pink or blue food dye to achieve the desired frosting color.
Transfer the frosting into a piping bag and snip off a large hole at the end. Once the cookies have cooled completely, frost them by piping a thick swirl from the center to the edges of each cookie. Use a butter knife to smooth out any rough edges. Repeat the frosting process for all the cookies and top them with colorful sprinkles of your choice.
Serve and enjoy your delicious frosted cookies!