Whisk flour, baking soda, and sea salt together in a large bowl; set aside. Beat butter, white sugar, and brown sugar with an electric mixer in a separate bowl until smooth. Add 1 egg and vanilla extract; beat until smooth. Mix in flour mixture until just incorporated. Fold in chocolate chips; mixing just enough to evenly combine. Form dough into tablespoon-sized balls; place onto a baking sheet, and freeze until solid, about 2 hours.

Preheat the oven to 350 degrees F (175 degrees C). Line 24 muffin cups with paper liners.

Lightly beat 3 eggs in a large bowl with an electric mixer. Add cake mix, water, and canola oil; continue beating for 2 minutes on medium speed. Spoon into prepared cupcake liners, filling each 2/3 full. Place a frozen cookie dough ball on the top center of each cupcake.

Bake in the preheated oven until a toothpick inserted into the cake portion of the cupcake (not the cookie dough ball) comes clean, about 20 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.