Preheat the broiler to high and position a rack in the top third of the oven.
Put the bacon in a 12-inch nonstick ovenproof skillet and place over medium heat. Cook, stirring often with a rubber spatula, until the bacon is crispy and golden brown, about 10 minutes. Remove the bacon to a plate with a slotted spoon and remove all but 2 tablespoons of the bacon fat from the skillet. Add the red onion to the skillet along with the hash browns. Stir in 1/2 teaspoon salt and spread the mixture evenly over the bottom of the skillet. Cook, undisturbed, until the potatoes are beginning to brown and get crispy, about 3 minutes. Stir the potato mixture with a rubber spatula. Re-spread the mixture evenly on the bottom of the skillet and cook, undisturbed, to brown a bit more, another 2 minutes. Add the kale and another 1/2 teaspoon salt and cook until the kale is wilted, another 2 minutes. Stir in the reserved bacon.
Meanwhile, whisk together the eggs, heavy cream and remaining 3/4 teaspoon salt in a medium bowl. Add the grated cheeses. Add the egg mixture to the skillet and stir to combine. Cook, stirring occasionally with a rubber spatula, until the mixture looks like loose scrambled eggs, about 2 minutes. Cook, undisturbed, to set the bottom, about 1 minute longer. Place the skillet under the broiler until the top is golden brown and the eggs are set, 3 to 4 minutes. Allow to cool for 5 minutes before slicing into wedges and serving.