In the bowl of a stand mixer fitted with the paddle attachment or in a large bowl with an electric mixer, cream butter, sugar, brown sugar and peanut butter until light and fluffy - about 3 minutes. Beat in eggs one at a time and add vanilla extract, mixing until incorporated.

In a large bowl, sift together flour, baking soda and salt. Gradually add the dry ingredients to the butter and sugar mixture and mix until thoroughly combined. Mix in oats and fold in the peanut butter chips. Cover and chill dough for at least 3 hours or up to 2 days.

When ready to bake, preheat the oven to 350°F and line baking sheets with parchment paper. You may need to let the dough rest at room temperature for 30-40 minutes before you can scoop the cookies out.

Using a large cookie scoop (3 tablespoons), scoop cookie dough onto prepared baking sheets, leaving a few inches between each cookie. Bake in preheated oven for 16-18 minutes, or until edges are golden brown. If desired, immediately sprinkle each cookie with a little flaky sea salt.

Allow cookies to cool on cookie sheets for 5 minutes before transferring to wire racks to cool completely.