Preheat the oven to 350°F (175°C).
In a saucepan, melt the butter over low heat.
Add granulated sugar and brown sugar to the melted butter, stirring until well combined.
Remove from heat and let cool slightly before whisking in the eggs and vanilla.
In a separate bowl, whisk together the oats, baking soda, and a pinch of salt.
Gradually fold in the oat mixture into the wet ingredients until just combined.
Line baking sheets with parchment paper and drop spoonfuls of dough onto the sheets, spacing them apart.
Bake in the preheated oven for 8-10 minutes, until edges are lightly golden.
Allow the cookies to cool on the baking sheets for a few minutes before transferring to a wire rack.