In a medium mixing bowl, use an electric mixer to blend the cookie mix, egg, softened butter and flour until well combined.
Cover and chill the dough for about an hour. Preheat the oven to 375 and roll the dough into 1-inch balls. Place the balls 2 inches apart on an ungreased cookie sheet. Press thumb in the center of each circle and bake for 8 to 10 minutes.
If the indentions puff up while cooking, use the back of a rounded tsp to re-press the centers immediately after baking. Cool cookies completely.
To make the caramel filling, combine the sugar, water and corn syrup in a medium saucepan. Bring to a boil over medium heat, stirring occasionally while boiling until the mixture turns a light amber color (about 4-5 minutes).
Remove from heat and add the cream and butter. Stir well and then add the pumpkin pie spice and canned pumpkin. Once the mixture is well combined, transfer to a covered container and chill in the refrigerator for at least 4 hours.
Spoon the caramel mixture into the cooled cookies and sprinkle each cookie with a bit of sea salt.