Place parsley, oregano, lemon juice, garlic, pistachios, ½ teaspoon salt, black pepper, red pepper, and 4 tablespoons oil in a mini food processor. Pulse until finely chopped and combined but still slightly textured, 6 to 8 pulses. Transfer to a small bowl.
Whisk together ricotta, Parmigiano-Reggiano, lemon zest, remaining 2 tablespoons oil, and remaining ¼ teaspoon salt in a separate medium bowl until smooth.
Fold each mortadella slice into quarters; thread onto 3 (10-inch) skewers, stacking slices snugly while gently separating edges to create ruffled layers.
Heat a large skillet over medium-high. Add butter and swirl until melted. Add skewers and cook, turning occasionally, until deeply golden with lacy, crisp edges, about 5 minutes. Remove from heat.
Spread fig jam onto bottom halves of toasted ciabatta. Remove mortadella from skewers and divide evenly among bottom halves. Spread ricotta mixture evenly on top halves of toasted ciabatta. Spoon pistachio mixture evenly over mortadella. Close sandwiches, and serve immediately.
