Preheat oven to 350 degrees. Brush a 10-by-15-inch rimmed baking sheet or jelly-roll pan with oil. Line bottom of pan with parchment, leaving a 1-inch overhang on the two shorter sides. Brush parchment with oil.
In a bowl, whisk together milk and flour. Add eggs, mustard, 1 teaspoon salt, and teaspoon pepper; whisk to combine. Pour into pan. Sprinkle spinach over top in an even layer.
Bake until edges of omelet are set, 10 to 12 minutes. Sprinkle with cheddar; bake until cheese has melted, 2 to 4 minutes. Beginning at one shorter end, lift parchment, and roll up omelet tightly, peeling back parchment as you go. Slice and serve.