In a skillet over medium heat, melt butter. When it starts sizzling, add diced apples and sauté for 2 minutes. Add brown sugar and salt; cook for 3 to 4 minutes or until the liquid is almost evaporated and the apples are soft enough to be broken with the tip of a wooden spoon. Transfer the apple mixture to a bowl to cool off; set aside.
Return the skillet over medium heat and add butter. When melted and hot, add flour and whisk for 2 minutes to remove the raw taste of it. Slowly pour in half-and-half, whisking constantly until there are no lumps and the sauce thickens. Reduce heat to low and add paprika, sea salt and freshly ground black pepper; whisk to incorporate. Remove from the heat and transfer to a large bowl and set aside; cool for 10 to 15 minutes.
Prep the cooking vessels by coating them with butter and then up the sides. Sprinkle Grana Padano cheese at the bottom and on the sides; set aside.
Add to the sauce, 2 egg yolks and cheese; stir to blend. Add the apple mixture and stir well; set aside.
In a medium stainless steel bowl, add 3 egg whites and a pinch of cream of tartar. Using a hand mixer, process until medium to stiff peaks form.
Add 1/3 of the beaten egg whites to the sauce and gently fold in until just incorporated. Add the remaining beaten egg whites and fold in gently until just mixed. Fill the cooking vessels about ¾’s full and place them on a baking dish lined with a silicone mat. Transfer to a 400ºF preheated oven at the bottom rack; bake for 22 to 25 minutes if using ramekins (4 ounces each) or 25 to 28 minutes if using cocottes (8 ounces each). Serve immediately.