Soak cashews for at least 2 hours, or overnight.
Preheat broiler. Halve and de-stem tomatoes and peppers, placing tomatoes cut-side-up on a rimmed sheet pan, with the peppers facing cut-side-down. Use 2 pinches of salt to lightly salt the produce.
Place under broiler, and completely char the skins of the peppers, and allow the tomatoes to char to about 30% to 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 over medium heat, add olive oil, onion, garlic, and salt. Sauté for 5–7 minutes, or until onions are translucent and golden brown.
When peppers are cool enough to handle, peel charred skin off and discard to your compost bin. Give remaining flesh a rough chop.
To a blender, add 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 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 bowls and top with additional fresh basil leaves.