Preheat oven to 375 degrees. Unwrap all the caramel candies and cut into quarters; set aside. In a medium bowl, whisk together flour, Chicharron Salt, and baking soda; set aside. In a separate bowl, using a stand or hand mixer, cream butter and sugars. Add vanilla and eggs, one at a time. Beat on high speed until mixture becomes pale and fluffy, about 2 to 3 min. Turn speed down to low and add in dry ingredients and caramel pieces. Mix until just combined. Cover and chill dough for at least 1 hour or up to 2 days.
Scoop rounded tablespoons of dough onto a greased or parchment-lined baking sheet, spaced about 1-inch apart. Sprinkle cookies generously with more Chicharron Salt. Bake for 10 to 12 min., rotating the sheets halfway through, until cookies are beginning to brown on the top. These cookies naturally spread so don't panic if your cookies come out flat! If baked until just starting to brown, they will remain soft. For crispier cookies, bake for 1 to 2 additional minutes. Let cookies cool and firm up on baking sheets, then transfer to wire racks to finish cooling. Enjoy warm or keep in an airtight container at room temperature.