Finely chop garlic and ginger in a food processor.
To the garlic-ginger mixture add the next 8 ingredients (cilantro through parmesan cheese) and puree until blended.
Add both oils through the food processor shoot to combine.
To make the salad:
Roast peppers under the broiler until charred on all sides (about 7-10 minutes), Put peppers in a bowl and cover with plasic wrap. Cool until easy to handle. Peel and seed the peppers. Chop peppers.
Combine peppers and remainder of salad ingredients. Mix with approximately one-half of the cilantro-lime dressing.