Preheat the oven to 350° and lightly grease a baking sheet(s).
In a medium bowl, whisk flour, baking powder and salt together. Set aside.
Using a large bowl, add softened butter, oil and sour cream, and beat on medium speed for one minute.
Add sugar and vanilla extract and beat until smooth.
Add dry ingredients into wet ingredients and mix on low speed just until dough forms a ball.
Using a two-inch cookie scoop, scoop out the cookie dough and place on the prepared baking sheet. Leave the rough looking edges.
Using the bottom of a glass, flatten each cookie a bit to produce even more of the jagged edges.
Bake for 10-12 minutes or until the edges are slightly browned.
Remove cookies from oven and let cool for 5 minutes and then remove and place on a wire rack to cool completely.
Buttercream Frosting
In a medium mixing bowl, cream butter, milk and vanilla together. Gradually add powdered sugar and beat until smooth and creamy.
Add gel coloring, stir, and add additional food coloring to get desired results, if desired.
Once cookies have cooled completely, frost cookies with a generous amount of frosting, then sprinkle with coarse sugar, add Easter sprinkles of your choice.
Let the frosting setup then place cookies in a container for storing and place parchment paper in between the layers.