1. Warm a wide, high-sided sauté pan over medium-high heat with 2 tablespoons of the olive oil. Season both sides of shrimp with salt and pepper. When oil is hot, add as many shrimp to the pan as will fit and cook just until shrimp turn bright pink and opaque. Remove shrimp from pan immediately; do not overcook. Repeat with remaining shrimp. Remove shrimp heads and reserve both bodies and heads. Do not rinse pan.
2. In a blender, combine shrimp heads (substitute 3 shrimp if you’ve used headless shrimp) with wine. Pass purée through a fine mesh strainer. Discard solids and reserve liquid.
3. Over medium-high heat, warm 1 tablespoon of the oil in the same sauté pan in which you’ve cooked the shrimp. Add coriander and, stirring continuously to prevent burning, sauté until fragrant, 1 to 2 minutes. Add 1 tablespoon of the oil, garlic, and onions, cover, and cook until translucent and soft, about 5 minutes. Add reserved shrimp-flavored wine, bring to a simmer, and simmer, uncovered, for 2 minutes. Add tomatoes with their juices and simmer for 15 minutes, stirring sauce frequently and breaking up tomatoes with a wooden spoon. Stir in lime juice and remaining 2 tablespoons oil. Taste, and season with salt and pepper. Keep over lowest heat.
4. Add lasagna squares to boiling water and cook until al dente, following manufacturer’s timing guidelines. Remove pot from heat, add spinach, and steep for 30 seconds. Drain and add to sauté pan along with shrimp. Gently toss all ingredients together and warm through, about 2 minutes.
5. Divide contents of pan among 4 plates; each serving will consist of about 8 handkerchiefs and 3 jumbo shrimp. You may also present everything in a large bowl and let your guests serve themselves.