Combine flour, salt, garlic and parmesan cheese in your food processor.
Pulse on and off until well combined.
Add blue cheese and butter; pulse until thoroughly incorporated.
Add 2 tablespoons water while machine is running.
Run the food processor until dough holds together. If too dry, add 1 more tablespoon water.
Transfer dough to a working area and shape dough into a log about 2-inches in diameter.
Wrap in aluminum foil and freeze for 1 hour.
Preheat oven to 400 degrees.
Line a baking sheet with parchment paper and set aside.
Remove dough from freezer and unwrap; set aside.
Combine egg and remaining 2 tablespoons water in a small bowl and lightly whisk until just combined.
Generously brush the dough with egg wash.
Roll or sprinkle the dough with sesame seeds.
Cut into 1/4-inch rounds.
Place on previously prepared baking sheet.
Brush the tops of the crackers with the remaining egg wash.
Bake for 13 to 15 minutes, or until edges are golden brown.
Remove from oven and cool completely on wire racks.