Preheat the broiler. Place the red and yellow peppers under the broiler and turn as they roast so it is even on all sides.
Place the roasted peppers in a small bowl, seal them tight with foil, and let them steam for 10 minutes. Remove from the bowl and pull off the skin. Use the back of a knife to remove the skin that will not come off. Remove the seeds, ribs, and s, and stems from the peppers. Chop them coarsely.
Melt butter in a soup pot over medium heat. Add the roasted peppers and leeks. Stir them in the butter to coat well. Reduce the heat to low and cook covered until the leeks are tender and translucent. About 5 minutes.
Add the potatoes, broth, and thyme. Bring to a simmer and cook partially covered until the potatoes are tender to be able to mash them with the back of a fork. 25 to 30 minutes. Remove any skim that comes to the surface. Keep the liquid level constant by adding more broth if need be.
Remove the pot from the heat and discard the thyme. With a handheld blender puree the soup. Bring back to a simmer over medium heat and add the heated cream.
Season with salt and pepper. Serve in warm bowls and garnish with chives and some diced peppers if on hand.