Puree cilantro, oregano, sugar, tomatoes, jalapeños, smashed garlic, and 2⁄3 cup water in a blender until smooth; set salsa aside.
Bring a medium saucepan of salted water to a boil, add potatoes, and cook until tender, about 25 minutes. Drain potatoes and transfer to a large bowl. Add minced garlic, butter, salt, pepper, and cumin, and mash until smooth. Set potato mixture aside.
Heat oil in a 12″ skillet over medium-high heat. Spread 1 heaping tbsp. potato mixture over half of each tortilla, and fold over to form a taco. Working in batches, add tacos to oil and fry, turning once, until golden brown and crisp, about 3 minutes.
Stuff cabbage, tomatoes, and cotija into tacos; drizzle with salsa before serving.