Preheat oven to 350°F. Line baking sheets with parchment paper.

In a saucepan over medium heat, melt the butter and brown sugar together, stirring until smooth.

Remove from heat and stir in the flour and salt until well combined.

Let the mixture cool for about 5 minutes. Then stir in the beaten egg and vanilla extract.

Mix in the rolled oats until evenly combined.

Place 1 tablespoon of batter on the baking sheet, ensuring there is at least 2 inches of space between each cookie. Use the back of a spoon to flatten each one into a thin circle.

Bake for 8 to 10 minutes, until the edges are golden brown.

Allow cookies to cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.