Heat one large skillet over medium-high heat. When pan is warm, add 2 tablespoons neutral oil and swirl pan to distribute oil across surface. Continue heating pan until oil is hot and shimmery.
Add diced onion and chopped bell pepper to skillet. Cook, stirring periodically, 5 to 6 minutes or until onions are translucent and peppers have softened. Note: stirring too frequently will prevent veggies from browning, fajita-style. If mixture begins to dry out or smoke, add 1 additional tablespoon neutral oil.
Once veggies are ready, reduce heat under skillet to medium. Add taco seasoning and stir until pepper and onions are well coated.
Add uncooked shrimp to skillet. Stir to incorporate, then cook shrimp 3 to 5 minutes, stirring occasionally, until shrimp are slightly curled and opaque with no pink in center.
Remove skillet from heat. Sprinkle fresh lime juice over mixture in skillet and stir to incorporate. Set skillet aside.
Heat other large skillet over medium heat. When pan is warm, add ½ tablespoon butter. Melt butter, swirling pan to distribute butter across surface. When butter is melted but not boiling or browned, place 1 flour tortilla in skillet completely flat.
Spoon approximately ⅓ cup shrimp mixture onto one half of tortilla. Top shrimp mixture with approximately ½ cup shredded cheese. Cook 90 seconds or until bottom of tortilla is lightly browned.
Use spatula to carefully lift opposite edge of tortilla from skillet. Fold tortilla in half, covering filling completely, and press lightly on top of quesadilla with spatula to keep tortilla folded.
Carefully place spatula under bottom half of tortilla and flip quesadilla over. Immediately sprinkle now-top of quesadilla with salt to taste.
Cook quesadilla 1 to 2 minutes or until other side of tortilla is lightly browned. When satisfied with doneness, carefully transfer quesadilla to large plate and set aside. Repeat process with remaining 5 flour tortillas until all quesadillas have been folded and melted.
Serve quesadillas warm with desired sides and toppings.