Place the oven rack 3 to 4 inches from the broiler element. Preheat the oven to broil.
Line a baking sheet with aluminum foil and place the red bell peppers on their sides on the prepared sheet.
Place the baking sheet under the broiler and roast the peppers for 5 to 6 minutes, or until the skin is deep brown.
Using tongs, carefully rotate the peppers. Continue broiling and rotating every 5 to 6 minutes until the peppers are evenly charred on all sides, about 20 to 25 minutes total.
Remove the peppers from the oven and tent loosely with aluminum foil to trap the heat and moisture.
Once the peppers are cool enough to handle, peel off and discard the skins.
Slice each pepper open and discard the seeds and stems. Dice the remaining flesh and set aside.
In a large pot or Dutch oven over medium heat, heat olive oil until shimmering.
Add the diced onion and cook, stirring occasionally, until softened and translucent.
Stir in the minced garlic, kosher salt, black pepper, and crushed red pepper flakes. Cook until the garlic is fragrant, about 1 minute.
Sprinkle in the smoked paprika and stir to coat the onion mixture evenly.
Add the diced roasted red peppers and vegetable broth. Stir well to combine.
Bring the mixture to a simmer and cook uncovered for 15 minutes to allow the flavors to meld.
Turn off the heat. Using an immersion blender, blend the soup directly in the pot until completely smooth. If using a countertop blender, let the soup cool slightly, blend in batches, and return to the pot.
Stir in the heavy cream and fresh lemon juice.
Warm the soup gently over low heat for 2 to 3 more minutes, stirring occasionally.
Ladle the soup into bowls and garnish with fresh basil leaves if desired. Serve warm.