How to Make It
Preheat the oven to 400°. In a small skillet, toast the pine nuts over moderate heat, shaking the pan, until golden, about 4 minutes. Transfer the pine nuts to a mini food processor and let cool. Add the arugula, Parmigiano-Reggiano, garlic and 1/4 cup of the olive oil and process until smooth. Season the pesto with salt.
Using a spoon, scrape the brown gills from the underside of the portobello mushroom caps. Place the mushrooms on a baking sheet, top side up, and brush with the remaining 1/4 cup of olive oil. Season the mushrooms with salt and roast for about 20 minutes, turning once, until tender. Let cool. Transfer the mushrooms to a work surface and thinly slice them.
Heat a panini press or griddle. In a small bowl, stir the cherry peppers into the mayonnaise. Spread the mayonnaise on the bottom halves of the ciabatta rolls. Top with the Taleggio, portobello and pesto and close the sandwiches. Cook the panini until golden and crisp outside and the cheese is melted within: 3 minutes in a press or 3 minutes per side on a griddle. Cut the panini in half and serve.