Preheat oven to 350 degrees F. Line baking sheets with parchment paper.
Cream butter and sugars together in a mixer. Add eggs, one at a time, mixing thoroughly between each one. Mix in vanilla. In a small bowl, dissolve the instant coffee granules in 1 tablespoon hot water. Add to the creamed mixture.
In a large bowl, mix coffee granules, flour, salt, baking soda and pudding mix. Add the dry ingredients to the creamed mixture and mix until just combined. Stir in the caramel bits.
Using a cookie scoop, drop dough onto the prepared baking sheets. Sprinkle dough generously with flaky sea salt. Bake for 10-12 minutes.