Using an electric mixer, cream the butter and sugar together until smooth.
Slowly beat in the flour until it is fully combined and is an even consistency.
Mix in the cheddar cheese and minced jalapeno pepper.
Divide the cookie dough in thirds. Roll each portion into an 8 inch log. Chill the logs in the fridge for 2 hours.
Preheat oven for 350F.
Cut each log into ½ inch cookie slices as seen in the photo above. You should get about 16 slices per log. Place the cookies on a cookie sheet lined with parchment paper.
Bake in the oven for 12 minutes. Cool on a wire rack.