Preheat the oven to 350°F. Combine the chiles, tomatoes, onion, garlic, chicken broth, vinegar, cumin, salt, and pepper in a small saucepan over medium-high heat. Bring the mixture to a simmer and cook for 2 minutes. Remove from the heat, cover the pan, and let the chiles steep in the liquid for 15 minutes. Transfer the chiles and liquid to a blender and blend until smooth.
Place the brisket in a large baking dish and spread the chile purée over the top. Add enough water to the pan to come ½-inch up the sides and cover tightly with aluminum foil. Roast for 1 hour, then reduce the oven temperature for 300°F and cook for another 3 hours, until the brisket is very tender.
Combine the vinegar, water, sugar, salt, mustard seeds, and coriander seeds in a small saucepan over medium-high heat, stirring until the sugar and salt are dissolved. Place the tomatillos in a small bowl. Once the liquid comes to a boil, pour over the tomatillos. Let sit at room temperature for at least 30 minutes.
Increase the oven temperature to 400°F. Brush the vegetable oil over the corn tortillas and arrange in a single layer on a large baking sheet. Bake for 10 to 12 minutes, until golden and crispy.
To assemble, shred the brisket into bite-size pieces and distribute the meat between the tortillas. Top each tostada some of the pickled tomatillos, cilantro, queso fresco, and a few slices of radish and serve.