Caramelize the white chocolate: Preheat the oven to 300°F / 150°C. Line a baking sheet with a silicone baking mat.

Distribute the white chocolate evenly over the prepared baking sheet. Bake for about 5 minutes, until they start to melt. Spread the chocolate with a spatula into a thin layer. Bake for another 5 minutes, then stir the chocolate. Repeat until the chocolate is the color of caramel. The chocolate may liquefy or it may become granular. If the chocolate is grainy, while still warm, put it in a coffee grinder or blender to smooth it out. It doesn't need to be perfectly smooth at this point. Place ⅓ cup / 57g in a small bowl and cool slightly. Place the remaining chocolate in the refrigerator to harden.

Make the cookie dough: In a stand mixer fitted with the paddle attachment, beat the butter and sugar at medium speed until creamy, about 3 minutes, stopping to scrape the bowl. Add the yolk and vanilla and mix until incorporated, about 1 minute. Mix in ⅓ cup / 57g of the softened caramelized white chocolate.

With the mixer on low speed, gradually add the flour and salt to the butter mixture, beating until just combined. Chop up the remaining chilled, caramelized chocolate and mix into the dough.

Divide the dough in half and form each piece into a log 1½ inches / 4cm in diameter. Wrap the dough in plastic wrap. Refrigerate for at least 1 hour, or up to overnight.

Preheat the oven to 350°F / 180°C. Line two baking sheets with parchment paper.

Slice the cookies into coins ⅛ inch / 3mm thick and lay them on the prepared baking sheets, spaced ½ inch / 2cm apart, so they have a little room to spread. Bake the cookies, one sheet at a time, in the middle of the oven for 8 to 10 minutes, until the edges are golden. Allow the cookies to cool completely on the baking sheets.