Roast half of the poblano peppers and half of the jalapeno peppers on the grill over medium heat for 3-4 minutes per side, just until beginning to brown and blister. Remove from heat and cool for about 10 minutes. (This step can be done several hours or a day ahead of time.)
Meanwhile, coarsely dice the raw poblano and jalapeño peppers.
Add pistachios to the food processor and puree until very fine. Add cilantro, basil and cheese and continue to process. Add both roasted and raw poblano peppers, jalapeño pepper, garlic, salt and lime juice and puree until smooth.
Finally, drizzle in olive oil and process one final time until smooth. There will still be some lumps, but mostly smooth.