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Preheat oven to 350F. Line 2 baking sheets with parchment paper.
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In a small bowl, whisk together the flour, baking soda, and salt; set aside.
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Using a stand mixer fitted with the paddle attachment, beat together the butter, brown sugar, granulated sugar on medium speed just until smooth, about 2 minutes.
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Beat in the vanilla and eggs, one at a time, until incorporated. Mix in the flour until just combined.
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Take about 1 tablespoon of dough and roll into a ball; place on prepared sheets. Repeat with remaining dough. Take a glass (or something with a flat bottom) and gently flatten each cookie.
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Bake, rotating the baking sheets midway through baking, until the cookies are very lightly browned in the centers, about 10 minutes.
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Let the cookies cool on the baking sheets until firm enough to handle, then use a spatula to transfer them to a wire rack.