Place an oven rack in the center of the oven. Preheat the oven to 325 degrees F.
Form the cookie dough into 12 equal-sized balls and place on an ungreased baking sheet. Bake for 16 to 18 minutes until lightly browned around the edges. Cool for 10 minutes. Transfer the cookies to a wire rack to cool completely, about 20 minutes.
In a small bowl, toss together the chocolate chips and oil. Place the bowl over a pan of simmering water and stir until the chocolate has melted and the mixture is smooth, about 3 to 5 minutes.
Spread the melted chocolate on top of 6 of the cooled cookies. Place on a parchment or wax paper-lined baking sheet. Sprinkle the chocolate-toffee candy pieces on top of the melted chocolate. Place the remaining cookies, flat-side-up, on the same baking sheet. Arrange the banana slices in a single layer on the flat side of the remaining cookies. Freeze all the cookies for 45 to 60 minutes until the chocolate has set and the banana slices are frozen.
Using an ice cream scoop, scoop about 1/3 cup softened ice cream on top of the frozen bananas. Place a chocolate covered cookie on top and gently press to form a sandwich. Repeat with the remaining ice cream and cookies. Freeze for 3 to 4 hours until firm.