Use 1 cup of the Nutella to make 2 teaspon sized dollops on a parchment lined sheet pan.
Freeze the Nutella dollops until firm.
Preheat the oven to 350 degrees F. Line 2 sheet pans with parchment or a nonstick silicon baking mat.
Place the butter, granulated sugar and brown sugar in the bowl of a mixer. Beat until fluffy, about 2-3 minutes.
Add the remaining 1/4 cup of Nutella and vanilla extract to the bowl. Beat until combined.
Add the egg and egg yolk to the bowl and mix until combined.
Add the flour, cocoa powder and baking soda to the bowl. Mix on low speed until just combined.
Scoop out 1 1/2 tablespoons of dough and form into a ball. Place on prepared baking sheets. Repeat with remaining dough.
Cover the pan with plastic wrap and freeze for 10-15 minutes or until balls of dough are firm.
Flatten each ball of dough with your hands and place a dollop of frozen Nutella on top.
Fold the dough around the Nutella and roll until smooth. Flatten each ball into a disc shape.
Place each cookie 2 inches apart on the baking sheets.
Freeze the cookies for 10-15 minutes or until firm.
Bake each sheet pan or cookies for 10 minutes. Let cool for 10 minutes then transfer to a cooling rack.
Place the dark and white chocolate into two bowls. Microwave each bowl in 30 second increments until chocolate is melted. Stir until smooth.
Use a spoon, piping bag or plastic resealable bag with the tip snipped off to drizzle both chocolates over the cookies.
Let cool until chocolate is hardened, then serve. Cookies can be stored in an airtight container for up to 3 days.