1. Prepare a grill for medium heat (350° to 450°). If using charcoal, add chips or wood chunks evenly over coals. If using gas, put chips or chunks in a shallow foil pan set on burner in corner of grill. Grill chiles, tomatoes, and onions, turning often, until skins blacken all over, 15 to 20 minutes.
2. Let vegetables cool, then peel. Stem and seed chiles. Chop vegetables and put in a medium pot with artichokes, herbs, purslane, vinegar, and 1/2 tsp. salt; bring to a boil, then cover and cook over low heat, stirring occasionally, until onions soften, 20 to 30 minutes. Remove from heat; let sit 1 hour, covered, so flavors can marry.
3. Purée roughly in a food processor, thinning with hot water to make it pourable. Let cool and season with salt to taste. Serve with oysters.
*Find red oak chips online from Susie Q's Brand (susieqbrand.com).
Nutritional analysis is per oyster with 1 tsp. salsa.
Make ahead: Up to 1 week, chilled.