Heat oven to 450°F. Generously spray a 13x9-inch rimmed sheet pan or glass/ceramic baking dish with cooking spray. Line with parchment paper, pressing the paper firmly into the bottom and sides of the pan (it should stick to all sides of the pan with the cooking spray; if it doesn’t, add more cooking spray). Spray parchment paper with cooking spray.
First, make the egg mixture: In a large bowl, whisk together milk and flour until no lumps remain. Add eggs, Dijon mustard, salt and pepper; whisk until well-combined. Pour the egg mixture into the prepared pan, and carefully transfer to the oven. Bake for 8 to 10 minutes or until the omelet is fully cooked through (it may puff up in the center and on the sides, but will deflate as it cools). To ensure food safety, eggs should be cooked to 160°F.
Next, add the toppings: Sprinkle cheese evenly over the top of the hot, cooked omelet. Cool 2 minutes in the pan to allow the cheese to melt and the omelet to cool slightly. Carefully, using parchment paper, transfer the omelet from the sheet pan to a cutting board or work surface, with parchment still underneath. Top omelet evenly with ham slices, baby spinach leaves and chopped red pepper.
Finally, assemble the roll-ups: Starting from one long end, roll up still-warm omelet tightly into a log, seam side-down, removing parchment paper as you roll it up. Allow omelet to cool completely, about 20 minutes.
Use a sharp, serrated knife to slice log into 8 equal-sized rolls. Serve immediately, or store in an airtight container in the refrigerator for up to 1 day before serving.