Place 10 tablespoons (140 g) butter in a small saucepan and melt over medium heat. Once melted, crank up the heat to medium-high. Stand by, continuously stirring and watching. Small golden bits will start to settle on the bottom of the pan. Once this happens, take it off the heat and pour it into a heat-safe, large bowl to cool until closer to room temperature, but still liquid.(For more details on browning butter, check out my How to Perfectly Brown Butter tutorial) Once the butter has cooled, add the oil, brown sugar, milk, vanilla and eggs and whisk until completely combined and the color has lightened, about 1 to 2 minutes. Add in the baking powder, baking soda and salt, whisking to combine, about 1 minute. Grab a spatula and fold in the flour until just combined and you still see small streaks of flour. Lastly, add in the chocolate chips and fold into the dough until evenly distributed. Lay a piece of plastic wrap over the top of the dough and let the dough chill in the fridge for 20 minutes.
Preheat your oven to 350°F (177°C). Cover several cookie sheets with parchment paper.
Scoop 3 tablespoons of dough and using your finger, press an indent in the center. Pace a chilled 2-teaspoon Nutella mound in the center and cover with the cookie dough. Set on the baking sheet leaving 3 inches (8 cm) between dough balls. If you have extra dark chocolate chips, set some over the top (I like to do this with my cookies so they look super chocolatey and delicious).
Bake in the center of the oven for 13 minutes or until golden brown around the edges. Let cool completely on the baking sheet. We slightly underbake these and let them finish baking and cooling on the baking sheet so we have a soft, chewy cookie with slightly crispy edges. Sprinkle with sea salt flakes (if using) and let cool completely on the baking sheet before serving.