Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper or silicone baking sheets.
Put the flour, sugar, baking soda, pepper, and thyme into a bowl and whisk together to combine. In a small bowl, whisk together the olive oil, milk, lemon juice, and zest. Add the liquid ingredients to the dry ingredients, stirring with a wooden spoon until you form a nice smooth dough.
Roll heaping teaspoonfuls of the dough into balls. Place them about 2 inches apart on the prepared baking sheets. Bake the cookies about 12 to 15 minutes, or until they are browned around the edges. Let the cookies cool for a few minutes and then transfer them to wire racks to cool completely.