Preheat oven to 425 degrees. Prepare 9-inch spring form pan (cover bottom with aluminum foil, attach sides of pan and tuck the foil underneath the pan bottom; coat the sides and bottom with Pam cooking spray) and set aside on rimmed baking sheet.
Whisk eggs, milk and 1/2 teaspoon salt in bowl until well combined. Stir in flour until just incorporated – the mixture will still be a bit lumpy. Whisk in butter until batter is smooth. Stir in scallions and set batter aside while preparing filling.
Toss potatoes with 1 tablespoon water in large microwave-safe bowl. Cover with plastic wrap, cut vent holes in plastic and microwave on high power until potatoes just begin to soften, 3 to 4 minutes. Meanwhile, cook sausage in large nonstick skillet over medium heat, breaking up clumps, until meat has lost most of its pink color, about 4 minutes. Using slotted spoon, spread sausage evenly over bottom of prepared spring form pan.
Heat oil in skillet with sausage fat over medium-high heat until shimmering. Add potatoes and 1/4 teaspoon salt and cook until potatoes are golden and crisp, 8 to 10 minutes. Drain potatoes on paper towels.
While potatoes are cooking, place spring form pan with sausage in oven for 10 minutes. Remove pan from oven and working quickly, sprinkle 1/4 cup cheese over sausage and pour batter evenly over filling. Scatter potatoes on top and sprinkle with remaining cheese. Bake until puffed and golden, 25 to 30 minutes. Remove pan from oven, run knife around edges of pan, and let cool 5 minutes. Release outer ring and, using spatula, transfer casserole to serving plate. Serve.