Combine cake mix, 1/2 cup melted butter, water and eggs in large bowl; beat at medium speed until smooth. Let batter rest for 30 minutes.
Heat oven to 400 degrees F. Drop batter by slightly rounded teaspoonfuls, 2 inches apart, onto parchment-lined or lightly greased cookie sheets. Sprinkle each cookie with sea salt. Bake for 5 to 7 minutes or until toothpick inserted in center comes out clean. Transfer to wire cooling rack.
Place 1 cup butter in medium bowl. Beat at medium speed until creamy. Reduce speed to low; gradually add powdered sugar. Beat until well mixed. Add caramel sauce, 1 teaspoon sea salt and vanilla. Beat until well mixed.
Pipe or spread rounded teaspoonful filling onto bottom of 1 cookie; place second cookie, bottom-side down over filling. Repeat with remaining cookies and filling.
Letting batter rest allows batter to rise and increase volume of whoopie pies. To make ahead, bake cookies as directed. Cool completely. Place cooled cookies in single layer in resealable plastic freezer bag. Freeze up to 2 months. Let stand at room temperature until thawed. Prepare filling and fill cookies as directed.