In a skillet, heat the oil on medium heat and cook the shallots until caramelized, about 10 minutes. Season with salt and pepper. Set aside.
For the popovers:
Place 6 ramekins on a baking tray and put a spoonful of duck fat into each ramekin. Place the tray in the oven and let warm for about 5 minutes so that the fat melts, but doesn't burn.
Meanwhile, mix the flour and salt in a bowl. In a saucepan, heat the milk on low heat for about 5 minutes.
In a large bowl, whisk the eggs until they get very frothy, 2 to 3 minutes. Slowly add the hot milk and continue to whisk. Stir the liquid ingredients into the flour mixture stirring the batter just until mixed. Do not over beat.
Take the pan out of the oven and pour the batter into each ramekin, about three quarters full. Divide the caramelized shallot mixture on top of each popover and cover with rosemary, grated Cheddar and freshly ground pepper. Bake in the oven until they start to look crusty and golden brown, about 15 minutes. Reduce the oven temperature to 350 degrees F. Continue cooking for about 15 minutes. Make a small incision in each popover 5 minutes before the time is up to release the steam and dry the inside of the popovers. The popovers will be puffy, light, and golden brown.