Preheat the oven to 350°F (175°C). Leave the cookie sheets ungreased.
Place the sugar cookie mix, dry butterscotch pudding powder, cooled melted butter, water, and egg in a large mixing bowl. Stir with a spoon only until the ingredients come together and form a soft dough.
Fold the butterscotch morsels gently into the dough, distributing them as evenly as possible without overmixing.
Scoop rounded tablespoonfuls of dough onto the ungreased cookie sheets, leaving approximately 2 inches of space between each portion.
Bake for 8–11 minutes. Remove the cookies when their edges appear set but the centers remain soft. Begin checking at the 8-minute point to reduce the chance of overbaking.
Immediately after removing the cookies from the oven, lightly scatter the coarse sea salt over their surfaces.
Allow the cookies to rest on the baking sheets for about 2 minutes. Transfer them carefully to wire cooling racks and leave them for approximately 20 minutes, or until completely cooled.