Prep the pan and oven. Heat the oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease well.
Cook the greens and aromatics. Warm the olive oil in a skillet over medium heat.
Add the onion and cook 3–4 minutes until soft. Stir in the mustard greens and a pinch of salt, and cook until wilted and most moisture evaporates, about 3–5 minutes. Set aside to cool slightly.
Mix dry ingredients. In a large bowl, whisk the flour, baking powder, baking soda, salt, black pepper, and smoked paprika until evenly combined.
Mix wet ingredients. In a separate bowl, whisk the eggs, buttermilk, yogurt, and melted butter until smooth.
Combine the batter. Pour the wet mixture into the dry.
Stir with a spatula just until a few streaks of flour remain. Fold in the cheddar, ham, and cooked greens and onions. Do not overmix.
Fill the tin. Divide the batter evenly among the 12 muffin cups.
They should be nearly full.
Bake. Bake 18–22 minutes, until the tops are golden and a toothpick inserted in the center comes out clean or with a few crumbs.
Cool. Let the muffins cool in the pan for 5 minutes, then transfer to a wire rack. Serve warm or at room temperature.