In a large shallow dish, combine 1 cup broth, chili powder, vinegar, cilantro, honey and seasonings. Add the pork; turn to coat. Refrigerate for 4 hours or overnight.
In an ovenproof Dutch oven, brown pork in 4 tablespoons oil in batches. Remove and keep warm. In the same pan, saute onions in remaining oil until tender. Add garlic; cook 2 minutes longer.
Return pork to pan; add remaining broth and tomatoes. Bring to a boil. Cover and bake at 350° until meat is tender, 1-1/2 to 1-3/4 hours. With a slotted spoon, remove meat to a large bowl. Skim fat from cooking liquid. Bring to a boil over high heat; cook until slightly thickened and reduced to about 2 cups, stirring occasionally. Return meat to pan; set aside and keep warm.
For sopes, in a large bowl, combine masa harina and salt; stir in water. Knead until smooth, adding additional water, 1 teaspoon at a time, if necessary. Divide into 12 portions, about 1/4 cup each. Roll each to form a ball; flatten to 4-in. patty. Cover with plastic wrap.
Heat a large ungreased skillet over medium heat until hot. Cook sopes in batches until lightly browned, about 1 minute on each side. Remove from pan. Immediately pinch edges to form a 1/2-in. rim; set aside.
To serve, in same skillet, cook sopes in hot oil in batches over medium-high heat until golden brown and slightly crisp, 15-30 seconds on each side. Drain on paper towels. Using a slotted spoon, place pork on sopes; serve with toppings of your choice.