Place the peppers directly over the flame of a gas-stove burner on high heat or on a grill. Roast peppers, turning with tongs, until blackened all over. (Alternatively, broil peppers on a baking sheet, turning as each side becomes charred.) Transfer to a large bowl, and cover immediately with plastic wrap. Set aside to steam 15 minutes. Peel peppers; discard skin. Remove stems, seeds, and ribs; cut each pepper into pieces. Set aside.
Heat oil in a large pot over medium-high heat. Add onions, garlic, and roasted peppers; cook, stirring occasionally, until onions are dark golden brown on the edges, 8 to 10 minutes. Stir in coriander, chili powder, and cayenne pepper; cook 30 seconds. Add sugar; cook, stirring occasionally, 2 minutes. Add tomatoes, 2 teaspoons salt, and 1/2 teaspoon pepper; cook, stirring occasionally, until tomatoes have broken down and are very soft, about 20 minutes.
Stir in the vinegar, mustard, honey, Worcestershire sauce, and soy sauce. Pour through a coarse sieve into a medium bowl, pressing out liquid with a spoon; discard solids. Return to stove, and bring to a boil. Reduce to a vigorous simmer, and cook, stirring occasionally, until reduced slightly and thickened, 15 to 20 minutes. Taste, and adjust for seasoning.
Sauce can be refrigerated in an airtight container up to 3 days.