Prepare two large baking sheets with a silicone mat (recommended) or cooking spray.
In the bowl of a stand mixer, cream butter and sugar together. Add egg and beat until smooth. Incorporate peanut butter, milk, and vanilla.
Sift in dry ingredients and mix until completely combined. Refrigerate dough 30-45 minutes.
Preheat oven to 350.
Using a medium cookie scoop, roll dough into 24 uniform balls. Roll balls in sugar.
Place the first dozen balls on prepared cookie sheets, 6 per sheet (they will spread). Place a thumbprint in each cookie. Using a teaspoon, scoop Nutella into each cookie, using your finger to scrape it carefully into the indentation.
Lightly flatten the remaining dozen balls of dough and place them over top of Nutella, like a blanket, covering the Nutella completely. Taking a large fork, lightly flatten cookies until they are more flat on top, rather than mounded, being careful not to press too hard and cause the Nutella to ooze out.
Bake 14-15 minutes until cookies began to turn golden on the edges, but still look slightly unset in the middle. Allow to cool 15 minutes before removing to a cooling rack. Cookies will be large.