Add flour, pepper, thyme, sugar, and salt to the bowl of a food processor and blend together.
Pour in olive oil and pulse a few times so dough begins coming together.
With the food processor on, pour in the milk and blend until a loose ball is formed.
Remove dough from food processor and wrap tightly in plastic wrap. Chill dough in refrigerator for about 1 hour.
Pre-heat oven to 375 degrees and line two baking sheets with parchment paper.
Split dough into two portions. Using one portion at a time, on a lightly floured surface, roll dough out into a large rectangle as thinly and evenly as you possibly can. The thinner you can get it, the better as it will result in a crispier cracker.
Lightly brush dough with egg wash and sprinkle sea salt on top.
Bake for 15-22 minutes, until crackers are getting crispy and turning golden. Check after 15 minutes. If crackers are still pliable and not totally crispy, return to oven, being sure to re-check every 2 minutes.
Let cool completely before breaking into pieces of whatever size you choose.