In a food processor, pulse together flour, paprika and salt. Add cheese and butter, pulsing until uniformly crumbly.
With the machine running, slowly pour in the milk. Dough should stick together when pressed with fingers.
Pour mixture into a large Ziploc bag (less messy!) and shape into a flattened disk. Chill for 40 minutes.
Take about ¼ cup of dough and shape into a ball with hands, gently warming it a bit. Flatten and place between 2 pieces of parchment paper (this works better than wax paper or plastic wrap). Roll out to 1/8” thick, and cut into squares (1" or 2" square) with cookie cutter, or pizza cutter. Repeat with remaining dough*. Place onto a parchment lined baking sheet and using the sharp end of a bamboo skewer, prick a few holes into each. If desired, you can sprinkle with a bit of water and shake some salt on their tops.
Bake at 375°F on the middle rack, for 12-14 minutes (depending on the size of cracker you made and its thickness).
Cool completely then store in an airtight container
Notes
*Because gluten free dough's have a strong tendency to tear and crack when rolled out, dividing the dough up into smaller portions allows for better handling (and less frustration!).