Heat oil in a large nonstick skillet over medium-high. Add bacon. Cook, stirring often, until lightly browned, about 4 minutes. Remove bacon with a slotted spoon to a paper towel-lined plate, reserving drippings in skillet. (Do not wipe skillet clean.) Return skillet to medium-high. Working in batches, add English muffin halves, cut sides down, to hot drippings in skillet. Cook until toasted, about 1 minute. Let muffin halves cool slightly.

Chop English muffin halves into bite-size pieces. Place on bottom of a lightly greased (with cooking spray) 13- x 9-inch baking dish. Sprinkle with cooked bacon. Finely chop white parts of scallions, and sprinkle over mixture in dish. (Wrap green parts of scallions in a damp paper towel; chill until ready to use.) Whisk together whole eggs, milk, pepper, and 1 teaspoon of the salt in a large bowl. Pour over mixture in baking dish; cover with plastic wrap. Chill at least 8 hours or up to 16 hours. 

Preheat oven to 350ºF. Let casserole stand at room temperature while oven preheats. Bake until top is browned and casserole is set, about 40 minutes. 

Meanwhile, make hollandaise. Melt butter in a small skillet over medium-low. Keep butter hot over lowest heat (do not let it brown). Process egg yolks, lemon juice, mustard, paprika, and remaining 1 teaspoon salt in a blender on medium just to combine, about 5 seconds. With blender running on medium speed, slowly pour hot, melted butter through center opening in blender lid. Process until mixture is smooth and thick, about 1 minute.

Drizzle about ½ cup hollandaise over warm casserole. Finely chop reserved green scallion parts, and sprinkle over top. Sprinkle with paprika; serve with remaining hollandaise.