Soak cashews for at least 2 hours, or overnight.
Preheat broiler. Halve and de-stem the tomatoes and peppers, placing the tomatoes cut-side-up on a rimmed sheet pan, with the peppers facing cut-side-down. Use two pinches of salt to lightly salt the produce.
Place under broiler, and allow to completely char the skins of the peppers, and allow the tomatoes to char to about 30%-40% of the surface. The peppers took the least amount of time, at about 5 minutes. I removed those to a cutting board to cool while the tomatoes continued cooking for an additional 5-8 minutes.
Using a large pot, turn heat to medium, add the olive oil, onion, garlic, and salt. Sauté for 5-7 minutes, or until the onions are translucent and golden brown.
When the peppers are cool enough to handle, peel the charred skin off, and discard to your compost bin, and give the resulting flesh a rough chop.
To a blender, add the soaked cashews, roasted red peppers, tomatoes, and onion mixture. Blend on high for about 30-60 seconds or until velvety smooth.
Add fresh basil, and blend for 2-3 seconds more to incorporate.
Return the blended mixture to the pot, and stir with a wooden spoon, scraping up any bits left from the onions. Heat through for 1-2 minutes.
Divide soup among four bowls, and top with additional fresh basil leaves.