Beat softened butter and Monterey Jack cheese at medium speed with an electric mixer until blended; add flour, beating until blended.
Divide dough into 3 equal portions; shape each portion into a 6-inch log. Cover and chill at least 8 hours.
Cut each log into 32 (1/8-inch) slices, and place on ungreased baking sheets. Gently press 1 pecan half into center of each wafer.
Bake, in batches, at 350° for 8 to 10 minutes. Remove crisps to wire racks to cool. Store in an airtight container. Prep: 30 min., Chill: 8 hrs., Bake: 10 min. per batch