Lightly butter a 9-by-13-inch baking pan, preferably a light-colored aluminum or steel pan. (Dark pans cause over-browning.)
Heat a large skillet over medium heat, add the butter, and cook until the butter foams and turns amber brown, 3 to 5 minutes. Pour the butter into a large bowl and set aside until cool enough to touch.
Meanwhile, sift the flour, baking powder, nutmeg and salt together into a bowl.
In the bowl of a stand mixer, or using a hand mixer, combine the brown sugar with the butter and mix until combined. Add the eggs and vanilla, and mix until smooth, thick and light, 3 to 5 minutes. (You want to make sure the mixture is very light and airy, like frosting.) Stir in the sifted flour mixture and mix by hand until incorporated.
Pour the batter into the prepared baking pan and spread it into an even layer, smoothing the top. Scatter the hazelnuts, pressing lightly to submerge them about halfway in the batter.
Bake until the surface wrinkles evenly and turns nut brown, about 35 minutes. Let cool completely, at least 2 hours, before cutting into 2-inch bars.
Adapted from "The New Midwestern Table" by Amy Thielen (c) Clarkson Potter, 2013. Provided courtesy of Amy Thielen. All rights reserved.