Preheat the oven to 375 degrees. Line a baking sheet with a silpat mat.
Combine the butter, olive oil, and egg together with a whisk until well combined.
Add the milk and grated apple then whisk.
Add the whole wheat flour and white flour; mix until just combined.
Add most of the cheddar, bacon, and parsley. Mix until combined.
Side Note: If it's too sticky, add a bit more flour. If it's too dry, add a bit more milk.
On a lightly floured work surface, knead the dough for 30 seconds until smooth.
Roll out the dough into a 10-inch circle, about 1/2 inch thick.
Sprinkle some of the remaining bacon bits, cheese, and parsley on the dough then lightly press down and place on the prepared baking sheet.
Using a bone-shaped cookie cutter, cut out the dog bones.
Bake until lightly golden, 20 minutes.
Transfer to a wire rack and cool completely.
Store in an airtight container in the refrigerator for up to 2 weeks or the freezer for 6 months.