Heat oven broiler to high. Brush bread slices with olive oil and toast on a sheet pan under broiler 1-2 min per side (watch closely, as bread will burn quickly). Remove bread from pan and set aside. Toss tomatoes with 1 T of olive oil, a pinch each of salt and pepper, and add to sheet pan. Return pan to oven and broil tomatoes until soft and blistered, approx. 5-6 min. Transfer tomatoes to serving platter, arranged around burrata, adding toasted baguette slices and several dollops of Arugula Pesto (recipe follows). Garnish with basil.
In a food processor, combine arugula, parsley, nuts and garlic until chopped well. Add cheese, salt and pepper. With the processor running, add olive oil in a steady stream until blended. Taste and adjust seasonings, as needed. Refrigerate in airtight container until ready to use.