Preheat oven to 350 degrees. Cut stems away from chard. Finely slice stems and cut leaves into thin strips, keeping stems and leaves separate; set aside.
Brush muffin halves with 2 T melted butter and place onto a sheet pan. Toast until golden. Place Serrano ham in a large pan and sauté over med-high heat until crispy, flipping once; set aside.
Add 3 T unsalted butter to the pan and keep at med-high heat. Add shallot and slices of chard stems; sauté until softened (approx. 3-5 min). Add remaining chard and 1/4 c of water; sauté until liquid has evaporated. Season with salt and pepper and set aside, keeping warm.
Pour cream into a saucepan over med-low heat and reduce to 1 1/3 c. Add egg yolks, one at a time, and whisk until sauce thickens slightly; do not boil. Remove from heat. Season with salt and pepper; set aside.
Fill a large pot with water halfway; bring to a boil. Add vinegar and lower to simmer (a rapid boil will cause the poached eggs to lose their shape). Break egg into a small ramekin, then gently drop egg into water. Repeat with remaining eggs and let cook undisturbed. Depending on desired doneness, poaching time will vary (approx. 5-8 min). With a slotted spoon, remove eggs and place onto paper towels.
To assemble, place 2 muffin halves on a serving plate and top each with chard, tomato, crisped ham then egg; dress with sauce. To warm, microwave on high 20-30 sec. Sprinkle with Manchego, chives and fresh ground black pepper.