Coat a large nonstick skillet with cooking spray and heat over medium.
Add the leeks, onion, and garlic, and cook for 5 to 7 minutes until soft.
Stir in the nutmeg and cook for 1 minute more.
Add the spinach and cook for 5 minutes.
Remove from the heat, season with salt and pepper, and stir in the lemon juice.
Transfer to a colander to cool completely.
Preheat your oven to 375°F (190°C). Lightly coat a baking sheet with cooking spray.
Once the spinach mixture is cool, squeeze out every last drop of liquid—this is key!
Transfer the dry spinach to a bowl and stir in the beaten eggs, feta, and Romano cheese until well combined.
Place one sheet of phyllo on your work surface and spray it lightly with cooking spray.
Top with a second sheet and spray again.
Repeat this process until you have a stack of 6 phyllo layers.
Shape half of the spinach filling into a log along one of the long edges of the phyllo stack, leaving a 1½-inch border.
Fold the short edges in over the filling, then roll the phyllo lengthwise into a tight log.
Place the strudel seam-side down on your prepared baking sheet and spray the top with cooking spray.
Using a sharp knife, cut shallow slashes about 1 inch apart across the top.
Repeat steps 3-5 with the remaining phyllo and filling to create a second strudel.
Bake for 40 to 45 minutes, or until the strudels are deep golden brown and crisp.
Let them cool on the baking sheet for 10 minutes before slicing and serving.
Keep your phyllo dough from drying out by covering the stack with a clean, slightly damp kitchen towel while you work.