Preheat oven to 400°F (200°C).

In a large bowl, cream butter and sugar together using an electric mixer until light and fluffy.

Beat in eggs and vanilla extract until well combined.

Gradually add baking powder and flour, one cup at a time, mixing well after each addition.

The dough will become very stiff. Finish blending the flour in by hand.

Do not chill the dough.

Divide the dough into two equal balls.

On a lightly floured surface, roll each ball into a 12-inch circle, about 1/8-inch thick.

Use cookie cutters to cut out desired shapes.

Place cookies on an ungreased baking sheet.

Bake on the top rack for 6 to 7 minutes, or until the edges are lightly browned.