Preheat oven to 400F. Roll out puff pastry on floured surface into an 8 x 12 inch rectangle. Trim uneven edges and lightly fold over sides to make a 1-inch border. Lightly press the middle in with your fingers. Bake until lightly golden, about 15 minutes.
In a bowl, mix the asparagus, scallions, olive oil, and spices.
Heat a grill pan on medium heat with a drizzle of olive oil. Sautee the garlic until it browns slightly, and add the asparagus mixture. Let it cook through, about 5-7 minutes.
Remove pastry from oven and lay asparagus spears crosswise, alternating sides into the hollow middle. Bake another 5-10 mins.
Coarsely sprinkle feta cheese on top while still hot. Garnish with thinly sliced lemon strips.