Heat the oil in a nonreactive saucepan. Add the onion and jalapeño and cook over moderate heat, stirring, until wilted, about 3 minutes. Add the ketchup, vinegar, sugar, mustard and Tabasco and bring to a simmer. Add the blueberries and simmer over low heat, stirring until thickened, about 10 minutes.
Puree the sauce in a blender or food processor until smooth. Pass through a strainer and season with salt and pepper. Serve at room temperature.
The sauce can be refrigerated for up to 1 day.
Any kind of beefsteak, hamburgers, pork chops, chicken.