Oven Warm-Up & Tortilla Toast : Heat oven to 400°F (205°C) with a parchment-lined sheet pan inside. On a dry griddle over medium, toast tortillas 45–60 seconds per side until pliable with light golden spots. Stack and cover with a towel.
Steam-Wilt the Greens : Add the tomato oil to the griddle/pan. Add spinach and ¼ cup water/broth; cook 4–5 minutes, stirring, until glossy and collapsed and most liquid has evaporated. (The splash of liquid softens the greens and prevents sticking.)
Flavor Build : Stir in garlic, lemon zest, and scallions; cook 2 minutes until fragrant. Season with oregano, basil, Aleppo, salt, and pepper. Stir in lemon juice. Spread the mixture into three neat mounds about 7–8 in (18–20 cm) across.
Blanket with Whites : Whisk egg whites (and the optional whole egg). Pour a thin layer over each spinach mound so the eggs reach the edges. Cook over medium-low 5–6 minutes until opaque and the edges lift easily; centers should read 160°F (71°C) or feel set.
Sheet-Pan Flip Assist : Scatter feta over the egg rounds. Lay one tortilla on each round and press 10–15 seconds. Invert each onto the hot sheet pan so tortillas face down, filling up.
Fold & Seal : Return to the oven 1 minute to re-soften tortillas. Fold the bottom third up over the filling, then fold the sides inward to form an open-ended envelope. Press seam-side down on the pan 45–60 seconds to hold shape.
Oven Finish & Rest : Bake wraps 3–4 minutes at 400°F (205°C) until the bottoms are lightly crisp and seams secure. Rest 3 minutes; serve warm with lemon wedges if desired.