Preheat oven to 350 degrees F.
In a mixing bowl, beat butter until light and creamy. Add sugars and beat until well combined. Add oil and eggs, mix to combine. Add dry ingredients and mix until just combined, dough will be thick.
Using an ice cream scoop, scoop cookie dough and gently roll into a ball shape, and place on the pan.
Once cookie dough is on cookie sheet, press the bottom of a flat glass into the additional 1/4 cup sugar, and then gently press into the cookie, to make an indentation. Repeat with remaining cookies.
Bake for approximately 9 minutes. Remove from oven and immediately press the bottom of the glass into each indentation again while hot. This helps create a well for the caramel. Allow to cool completely.
Unwrap caramel and place in a large microwave safe bowl with heavy cream. Microwave for one minute on high, remove from microwave and stir well. Repeat in 30 second increments, stirring after each, until caramel is smooth and melted.
Using a scoop, scoop some warm caramel into the well on top of each cookie. If desired sprinkle with sea salt flakes. Allow caramel to cool in order to set. These cookies are best when stored flat and not stacked.