Preheat oven to 350 degrees. In the bowl of an electric stand mixer fitted with the paddle attachment and set on medium-high speed, whip together butter, granulated sugar and vanilla extract until mixture is pale and fluffy, about 4 minutes.

Add egg yolks to butter mixture and blend. Set egg whites aside in a small bowl.

With mixer set on low speed, slowly pour in flour and mix until combined {mixture will seem dry at first but will start to come together}.

Using a 1 teaspoon size cookie scoop, form dough into cookie balls and place on a large plate or sheet pan. Set in the refrigerator and allow to chill for 30 minutes.

Whisk egg whites with 2 teaspoons of water until frothy. Place chopped pecans in a shallow bowl. Remove cookie dough balls from refrigerator. Dip the top of each ball into the egg whites. Press the top of the cookie into the pecans and place each cookie on a sheet pan lined with a silicone baking mat or parchment paper, fitting 12 cookies per sheet.

Using your index finger, make an indentation in the center of each cookie, pressing the top together a bit to make sure the indentation is round. Fill each indentation with a 1/2 teaspoon of the peach butter {or preserves}.

Bake cookies for 14 - 16 minutes, rotating pans once during cooking time. Allow to rest on baking sheet several minutes before transferring to a wire rack to cool.

While cookies are cooling, prepare the brown butter glaze.

Place butter in a small skillet over medium heat. Once the butter has completely melted, watch closely. As butter starts to brown, begin swirling the pan on the burner. Allow the butter to brown for about 2 minutes, swirling constantly. Remove from heat.

In a clean bowl, combine the powdered sugar and salt. In a glass measuring cup combine the browned butter, 4 tablespoons of milk and vanilla. Whisk until combined. Pour the milk and butter mixture into the powdered sugar mixture. Whisk until smooth. If a looser consistency is desired, keep adding splashes of milk until it looks good to you.

Drizzle each cooled thumbprint cookie with the browned butter glaze.