Preheat oven to 375 degrees F.  Line two cookie/baking sheets with parchment paper. In a large bowl, combine butter, olive oil and egg. Add milk and grated carrot.  Add whole wheat flour to carrot mixture until just combined. Add the cheddar cheese, bacon and parsley.  Mix well. Turn dough onto a lightly floured board.  Knead the dough for about 30 seconds.  Roll the dough out until it’s about 1/2-inch thick. Use cookie cutters (preferably bone-shaped) to cut out dog biscuits. Arrange cut biscuits on the prepared baking sheet, about 1/2-inch apart.  The biscuits can be spaced closer together than regular cookies, since they won’t spread during the bake time. Bake for 23-27 minutes or until light golden brown. Cool completely on a wire rack.  Store biscuits in an air-tight container in the refrigerator up to 2 weeks.  Biscuits can also be frozen after cooling.