Heat reserved oil in heavy large skillet over medium-high heat.
Add chicken and saute 5 minutes
Add poblanos and saute 2 mintues.
Add tomatoes, 1/4 C basil, prosciutto and 2T cooked garlic... saute until chicken is cooked through, about 1 minute.
Remove from heat, add butter and stir just until melted.
Cook linguine in large pot of boiling salted water until tender but still firm to bite.
Drain linguine and place in large bowl.
Add chicken mixture and 1/2 C Parmesan, toss to coat.
Season with salt and pepper. Sprinkle with remaining 1/4 C basil and 2 T cooked garlic.
Serve with remaining Parmesan.
Serves 4.