Preheat your oven to 250˚ Fahrenheit. Line a sheet pan with parchment paper and place the white chocolate morsels onto the pan. Toast the white chocolate morsels for 40 minutes, stirring once half way through, until the chocolate is a light golden color. Remove the chocolate from the oven and allow it to cool.
While the chocolate is toasting, place the butter in a saucepan over medium heat. Heat the butter, stirring constantly until it reaches a light golden brown and then remove it from the heat. Allow the butter to cool to room temperature. (It will still be a liquid.)
Warm the cream (or milk) until it is scalding hot. Pour the cream over the toasted white chocolate morsels. Stir until a smooth ganache forms. (You may use a food processor or an immersion blender if desired.) Pour the ganache into a shallow bowl or a silicone mold and place in the freezer to harden.
Place the browned butter and brown sugar in a mixing bowl. Beat until a creamy mixture forms. (2-3 minutes) Add the eggs one at a time and beat until smooth. Add the salt, vanilla, and baking soda and mix again until combined.
Add the flour and mix until the dough is just coming together. Stop and add the dark chocolate chunks.
Divide the cookie dough into about 30 even pieces, and roll each piece out into a 3-4 inch circle.
Spoon about a teaspoon of ganache into the center of each cookie dough circle. (The ganache will be a little sticky, almost like a caramel or taffy even though it is frozen, this is because of the sugar content.) Pinch the circle into a ball, trapping the ganache inside. Freeze the cookie dough balls for at least 30 minutes.
While the cookie dough balls are freezing, preheat the oven to 350˚ Fahrenheit. Line some cookie sheets with parchment paper. Place the frozen cookie balls onto the sheets and bake for 8-11 minutes or until the edges are a faint golden brown.
The cookies will keep for up to 5 days in an airtight container.