Heat the broiler. Line a sheet pan with non-stick aluminum foil or spray it with cooking spray.
Remove the stem and seeds from the bell peppers. Cut the pepper in 2-4 slices and remove the white veins.
Place the bell pepper slices on the sheet pan skin side up.
Place the sheet pan in the oven. Remove the tray once the skin of the peppers has turned black. Cooking time may vary, so keep an eye on them. They should be done within 10-20 minutes.
Put the peppers in a bowl and cover with a plate, aluminum foil, or plastic wrap.
Once the peppers have cooled, peal the skin off. Be sure to remove as much of the skin as possible.
Heat the olive oil in a medium skillet over medium-high heat.
Add the shallots and season with a pinch of salt. Cook for about 2-3 minutes until they are soft. Add the garlic and stir for another 1-2 minutes.
Place the peppers in the skillet along with the smoked paprika, kosher salt, and pepper and stir.
Pour in the white wine and chicken stock. Allow that to cook until the liquid is reduced by half, about 5 minutes.
Add the contents of the skillet to a blender or a processor. Add the butter, vinegar, and cream. Blend until smooth.
Taste the sauce. Make any needed adjustment to the salt or vinegar.
Serve immediately or refrigerate up to 1 week.