To make pasta salad
Preheat a grill or grill-pan. Insert grape tomatoes onto skewers. Brush with the olive oil. Grill over direct medium-high heat until rich grill marks form, about 8 minutes.
Meanwhile, boil pasta per package directions (ideally in salted water), for about 10 minutes. Drain, toss with ice cubes to cool, then drain again.
Toss the cooled pasta with the pesto. Then toss with the arugula, grilled grape tomatoes, sea salt, and pine nuts. Adjust seasoning.
Serve with the lemon wedges.
To make fresh basil pesto
In a food processor, pulse all ingredients except olive oil until finely chopped.
Then drizzle in olive oil and puree until desired consistency. Makes 1 cup. Freeze extra pesto for later use.