Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil.
Place the pepper onto the prepared baking sheet. Cook under the preheated broiler until the skin of the pepper has blackened and blistered, 5 to 8 minutes. Turn pepper over to blacken all sides. Place the blackened pepper into a bowl and tightly seal with plastic wrap. Allow the pepper to steam as it cools, about 20 minutes. Cut the pepper in half and remove seeds; strip and discard skin from pepper, chop, and set aside.
Heat olive oil in a saucepan over medium heat. Stir in the garlic; cook and stir until fragrant, about 30 seconds. Add green onion and roasted red bell pepper; cook and stir for 3 minutes. Stir in peas and cook for another 3 minutes.
Pour in vegetable broth, bring to a boil, reduce heat to low, and simmer until peas are tender, about 8 minutes. Stir in basil, remove from heat, and let cool. Pour pea mixture into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth. Return soup to pot over medium heat and cook until heated through; season with salt and cracked black pepper to taste.
I buy vegetable broth in a 14-ounce can, pour it into a measuring container, and add water to equal 2 cups.