Combine flour and salt in a large bowl and cut in the butter with a pastry blender or a fork until it resembles corn meal. Stir in the milk a tablespoon at a time until the dough holds together without being wet or sticky. Test by squeezing a small amount of dough together; if it is still too crumbly, add a bit more milk, 1 tablespoon at a time.
Turn out dough onto a clean work surface. Divide in half, and place each half on a sheet of plastic wrap. Shape into flattened disks. Wrap in plastic, and refrigerate at least 1 hour, or overnight.
Once chilled, roll out the dough to ⅛-inch thick and cut with a 4-inch biscuit cutter (or a bowl around that size). Re-roll the scraps and cut. You’ll get about 8 or 9 rounds per disk of dough.
Whisk the egg in a small bowl. Place a heaping teaspoon of guava paste on each round of pastry. Brush a bit of egg on the edges and fold the pastry over the guava paste. Use a fork to press and seal the seam.
Pour 2 inches of oil into a deep skillet or Dutch oven. Heat to 375°F. Fry pies a few at a time without overcrowding the pan until golden brown on each side.
Remove and drain on paper towels. Sprinkle with powdered sugar if desired.