Brown Butter Hazelnut Sugar Cookies

Adjust oven rack to middle position and heat oven to 350 degrees. Line 2 large rimmed baking sheets with parchment paper. Whisk flour, baking soda, baking powder, and salt together in medium bowl. Set aside.

Place 1½ cups sugar, hazelnuts, and cream cheese in large bowl. Place remaining 1/3 cup sugar in shallow baking dish or pie plate and set aside. Heat butter in 10-inch skillet over medium-high heat until melted, about 2 minutes. Continue to cook, swirling pan frequently, until butter is dark golden brown and has nutty aroma, 1 to 3 minutes. Pour butter over sugar and cream cheese mixture; whisk to combine (some small lumps of cream cheese will remain but will smooth out later). Whisk in oil until incorporated. Add egg, milk and vanilla; continue to whisk until smooth. Add flour mixture and mix with rubber spatula until soft homogeneous dough forms.

Divide dough into 24 equal pieces, about 2 tablespoons each. Using hands, roll dough into balls. Working in batches, roll balls in reserved sugar to coat and set on prepared baking sheet, 12 dough balls per sheet. Using bottom of drinking glass, flatten dough balls until 2 inches in diameter. Sprinkle tops evenly with 4 teaspoons reserved sugar (2 teaspoons per tray), discarding any remaining sugar.

Bake, 1 tray at a time, until edges are set and just beginning to brown, 11 to 13 minutes, rotating tray after 7 minutes. Cool cookies on baking sheets 5 minutes. Using wide metal spatula, transfer cookies to wire rack and cool to room temperature.