Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, cream together the softened butter, light brown sugar, and granulated sugar using an electric mixer on medium speed until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract until combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, salt, and instant espresso powder.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.
Stir in the rolled oats and chopped walnuts (if using) by hand with a spatula until evenly distributed.
Using a tablespoon or cookie scoop, drop rounded spoonfuls of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are golden brown but the centers remain soft.
Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.