Make the salsa: Combine the tomatoes, onion, jalapeno, cilantro and 1 teaspoon salt in a bowl.
Preheat the oven to 200 degrees. Make the corn cakes: Warm the milk and butter in a small saucepan over low heat just until the butter melts. Combine the masa harina, 1 teaspoon salt, the sugar and queso fresco in a large bowl. Stir in the milk mixture to make a soft dough. Scoop the dough into 8 portions (about 1/4 cup each) and place on a parchment-lined baking sheet. Cover with another sheet of parchment; press a pan on top to flatten into disks.
Heat 1 tablespoon olive oil in a large nonstick skillet over medium heat. Working in batches, fry the corn cakes until crisp and golden on the bottom, about 3 1/2 minutes; flip, press lightly with a spatula and cook until golden on the other side. Continue with the remaining cakes, adding more oil as needed. Season the cakes with salt; place on a baking sheet and keep warm in the oven while you poach the eggs.
Bring a deep pan of water to a simmer over medium-low heat; add the vinegar. Poach the eggs.
Divide the corn cakes among 4 plates; top each cake with a poached egg, salsa and cheese; serve with avocado.