Cut the butter into cubes and put into a stainless steel saucepan or skillet. Melt over low heat and cook until it starts to turn a golden brown, with brown flecks in the butter. Transfer to a heat safe container, let cool for about 5 minutes, and add the half and half.
Put the sugars in a mixing bowl and add the cooled butter mixture to the mix. The butter should be slightly warm, but not too hot to touch. Add the eggs one at a time, mix well, and then add the vanilla. The butter will rise, and it will seem like it’s not coming together, but this is fine.
Combine the flour, salt, baking soda, and coffee granules and whisk. Add this to the butter/sugar mixture.
Mix until all of the flour is combined and you have a thick, caramel colored batter. Stir in both of the chocolates.
At this point, either scoop the dough onto parchment lined cookie sheets, or chill in the bowl. Let chill at least 12 hours, but 24 will give you better cookies. If scooping after chilling, take the dough out of the fridge for 20 minutes beforehand to ease the scooping process.
When ready to bake, preheat the oven to 375.
Bake for 10 minutes, and remove from the oven. Immediately sprinkle with coarse sea salt, and press lightly into the warm dough. Let cool on a wire rack.