Preheat oven to 325 degrees. Lightly spray 48 mini muffin cups with nonstick cooking spray. Pat the maraschino cherries dry with paper towels.
In the bowl of a food processor, combine the 1 cup of butter and cream cheese and process until blended. Add the flour and 1/8 teaspoon salt to the processor and blend until mixed. Do not over-process.
Using a small ice cream scoop or spoon, scoop out about 1 tablespoon of dough per cookie and roll into balls. Place the balls into the prepared muffin tins. Using your thumb or the end of a French rolling pin, make an indentation in each ball.
In a small bowl, whisk together the 2 tablespoons reserved maraschino cherry juice, the 1 tablespoon melted butter, remaining 1/8 teaspoon salt, sugar, egg and vanilla extract. Put about 3/4 teaspoon of the mixture into each dough ball indentation. Place a maraschino cherry in each cookie with the stems up.
Bake for 25 minutes or until the cookies are lightly browned and the filling is set. Let cool in the pans for 5 minutes and then remove to a wire rack to finish cooling.
For gluten-free: Substitute for the 2 cups flour:
1 cup superfine white rice flour
1/3 cup superfine sweet rice flour
1/3 cup millet flour
1/3 cup potato starch (not potato flour)
1 teaspoon xanthan gum
In a large mixing bowl whisk together the flours, starches and xanthan gum. If using an all-purpose gluten free flour in place of the flours and starches, omit this step. Add to the butter and cream cheese instead of regular flour, in the recipe above.