Combine the chiles in a large bowl and add enough water to cover them (I use hot but not boiling water). Soak the chiles until they’re soft, about 30 minutes. Drain and discard the soaking water.
Place the drained chiles in a blender. Add the 1/2 cup water, ginger, salt, cumin, and pepper and blend until smooth, stopping and scraping down the pitcher with a rubber spatula as needed, about 1 minute. (The mixture will be thick—don’t add extra water.) You will yield about 1 cup of chile purée.
Put the chicken in a bowl, add 1/2 cup of the chile puree (the rest can be refrigerated for a week or frozen for a few months to make another batch of tacos in the future), and rub it onto the chicken until the meat is well coated. At this point you can cook the chicken right away, or cover and refrigerate it for up to 24 hours.
Preheat a grill, griddle, or large skillet over medium heat. Add just enough oil to add a thin sheen to the grill grates or pan. Season the chile-slathered breasts with salt and cook, in batches if necessary, until they’re well browned on both sides and just cooked through, turning them over once, 8 to 10 minutes per batch. Let the chicken rest for a few minutes, then slice or dice it for tacos, and serve with the tortillas and your choice of garnishes.