Heat the oven to 350°F (175°C) and line baking sheets with parchment paper.

Beat softened butter and granulated sugar until light and creamy, about 2 minutes. Mix in the egg yolks and vanilla, then add the flour and salt and mix just until a soft dough forms.

Shape the dough into approximately 1-inch balls. Dip each ball in lightly beaten egg white, then roll it in finely chopped pecans, pressing gently so the nuts adhere.

Arrange the coated dough balls about 2 inches apart on prepared baking sheets. Press a deep indentation in the center of each cookie with your thumb or the rounded end of a measuring spoon.

Chill the shaped dough for 20–30 minutes if it feels soft. Bake for 10–12 minutes, until the edges are set and lightly golden, pressing the centers down again while warm if they puff.

Melt the caramels with the heavy cream or milk in the microwave in short intervals, stirring between each interval until smooth. Spoon or pipe a small amount into each cooled thumbprint.

Melt the chocolate chips, adding the shortening or coconut oil if desired for a thinner drizzle. Drizzle the chocolate over the filled cookies and let the topping set before serving.