• Dice the stems of the chard, and slice the leaves.
• Heat a large skillet on medium-low heat; heat the butter and oil until melted.
• Add the onions with a pinch of salt and pepper. Cook, stirring occasionally until the onions become translucent, about 5 minutes.
• Bring the heat up to medium-high, and add the stems with 1/4 cup water, cover and cook until soft, about 8 to 10 minutes.
• Add the chard leaves with 1/2 teaspoon salt; cook until wilted, about 2-3 minutes. Set aside on a dish and keep warm.
• To the skillet on medium-high heat, add the ham and cook until lightly browned on each side, about 1 minute. Set aside.

Meanwhile, for the Poached Eggs:

• Crack eggs into individual small cups or ramekins.
• Bring a pot of water to a boil. Add vinegar and salt. Reduce to simmer.
• Use a spoon to stir the water so it is spinning around in a circle. This will keep the egg whites from spreading out away from the yolk.
• Carefully drop eggs one at a time into the center of the pot.
• Simmer for 2 minutes then turn off the heat. Cover and let sit for 2 more minutes.
• Gently remove eggs with a slotted spoon and place on plate lined with paper towels.
• Divide the muffin half among 4 plates.
• Top each muffin half with a piece of ham, 1/4 of the chard and top with 1 egg.