Preheat oven to 450°F and line a baking sheet with parchment paper or a silpat liner.
Whisk together the flour, baking powder, salt, and thyme in a large bowl.
Cut in the butter with a fork, two butter knives or a pastry blender until the butter is mostly incorporated. Stir in the shredded cheese and cubed turkey until it’s completely coated with flour.
Use a fork to mix in the cream and then the milk until the dough comes together; knead it a couple times with your hands.
The dough should come together, but not be too wet. If the dough is too crumbly, add milk a little at a time until it comes together.
Turn the dough out onto a lightly floured surface. Roll or press the dough out to a circle about 7 to 8 inches in diameter and 3/4 inch thick. Use a floured 2 1/2 inch round cookie cutter to cut out the scones, gathering up the scraps of dough and reworking as necessary.
Transfer the scones to the prepared baking sheet, lightly brush the tops with milk.
Bake until the scones are puffed and light golden brown on top and bottom, about 14 to 16 minutes.