Combine Aleppo pepper, sherry, olive oil, zest and dill in a medium-size bowl. Add shrimp and toss to coat. Marinate for about 30 minutes.
Heat a large skillet over medium heat. Season shrimp to taste with salt and pepper. Add to skillet in batches if needed, and cook until they brown and just lose their translucency, about 2 minutes per side. Move skillet off the heat; transfer shrimp to a warmed dish then tent with foil to keep warm.
Meanwhile, drain cheese and add to the still-warm pan. Gently stir mozzarella balls to coat and slightly warm, scraping the pan to incorporate the browned bits. Add mozzarella to the shrimp. Season with salt and pepper, and brighten with a squeeze of lemon, if desired. Stir in the red bell pepper. Serve immediately.
Note: Aleppo pepper - a crushed chile with moderate heat and a fruity characteristic - is seedless, and somewhat moist and oily. It can be found in Middle Eastern stores and some specialty grocers. You can substitute a similar chile like marash. Fresh buffalo mozzarella comes in several diameters including ciliegene, which is cherry tomato-size (around 1 1/2 inches), and a size similar to the shrimp. Or, cut a larger fresh mozzarella ball into bite-size pieces.
Wine pairings: For everyday, try the 2009 Barone Fini Alto Adige Pinot Grigio (around $12) imported by W.J Deutsch & Sons. For company, seek out the 2009 Babcock Sta. Rita Hills Sauvignon Blanc ($18); and for a splurge, try the Bodegas Gerardo Mendez's 2008 Do Ferreiro Rias Baixas Albarino (around $23), imported by De Maison Selections.
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