Heat oven to 400 degrees F. Cut butter into flour and salt in a large bowl using a pastry blender or two knives. Blend until butter is in tiny pieces, then add 3 to 4 tbsp cold water and stir until dough just comes together. Form dough into ball; wrap and chill for 1 to 2 hr.
Divide dough into 24 pieces and roll into balls. Press into mini muffin tins, pressing dough into the bottom and up the sides in an even layer.
Bake 10 min, remove from oven and use a pestle or rounded side of a teaspoon measure to press down each tart shell. Bake until golden brown, about 10 min more.
In a food processor, blend cheese, Parmesan, a pinch of pepper, thyme and enough milk to make a smooth mixture. Spoon into cooled shells.
Cut beets into tiny dice; top cheese with beets and garnish with thyme. Makes 24 tarts.