Coat a 13x9-inch baking pan with 2 tablespoons of the softened butter. Spread the butter out to coat the bottom of the pan.
Arrange the dinner rolls in the prepared pan. Brush the top of the rolls with the oil.
Coat a piece of plastic wrap with cooking spray (or more oil) and arrange over the rolls, oiled-side down.
Let the rolls rise in a warm, draft-free place until they have doubled in size, about 3 to 5 hours. The actual time will depend on the temperature of your kitchen.
Preheat the oven to 350 degrees.
Remove and discard the plastic wrap. Using your fingers, punch the rolls down, deflating them while making fingerprints (dimples) in the dough, all the way to the bottom of the pan.
In a small bowl, combine the remaining 2 tablespoons of softened butter, brown sugar, and cinnamon and mix well (use your fingers to create a fine crumble). Sprinkle the mixture all over the top of the dough.
Bake for 20 to 25 minutes, until puffed up and golden brown.
Meanwhile, to make the glaze, in a medium bowl, whisk together the powdered sugar, heavy cream, and vanilla until smooth. If you prefer a thinner glaze, whisk in more cream (or milk).
Cool the focaccia for 5 minutes before drizzling some of the glaze over top. Serve the remaining glaze on the side.