Preheat a medium heavy griddle or cast-iron pan over medium-high heat. Add the whole tomatoes, serrano chile and shallot and roast on the dry skillet, turning frequently, until golden brown on all sides, about 8 minutes.
Transfer the vegetables and chile to a food processor and add the chicken broth and cilantro. Pulse until smooth but with some small pieces remaining, or to the desired consistency. Season with salt and pepper.
Serve immediately or cool to room temperature and store in an airtight container in the refrigerator for up to 5 days.