Preheat the oven to 350 degrees.
Line a standard 12 count muffin tin with parchment liners.
Melt the butter over low heat in a skillet. Add in the diced apples and cook over low-medium heat for 5 minutes until fork tender (but not soft and mushy). Stir in the sugar, brown sugar, and cinnamon. Cook for 1-2 more minutes stirring very frequently. Stir in the 1 & 1/2 tablespoons of flour. Turn off heat and set aside.
Using the smallest holes on a box grater, shred the Old Croc Sharp Cheddar (enough to yield 2 cups). Place into a large bowl.
Cut the butter into very small cubes. Add to the cheese. Add the flour and sifted powdered sugar to the mix.
Using a pastry blender or your hands (I prefer using my hands), work all of the ingredients together until large crumbs form. This will take a few minutes and some elbow grease. You will be working the dry ingredients into the cheese and flour. Once the crumbs have come together, loosely measure out 2 & 1/2 cups of the crumbs (do not pack the dough down). Set the extra dough off to the side. Measure out 2 tablespoons of dough into each muffin liner. Press the dough firmly into the bottom of each liner.
Evenly distribute the cooked apples into each muffin spot.
Using the reserved dough evenly sprinkle the crumbs over each tart.
Bake on the center rack of the oven for 25 minutes.
Remove from oven. Allow to sit for 5 - 10 minutes before serving. These tarts are best served warm with a scoop of ice cream or whipped cream (optional)