Note: You can make the pasta rounds up to a day ahead: Dust with flour, stack them in the shortest possible layers with pieces of plastic wrap between layers, cover well with plastic wrap, and refrigerate until ready to use.
Mix 1 1/4 cups flour, whole eggs, and cream to form dough. Turn out onto a clean surface and knead until smooth, about 5 minutes. Cover with plastic wrap and set aside 30 minutes.
Meanwhile, bring a large pot of water to a boil. Prepare a large bowl of ice water and set it next to the stove. Add 1 tbsp. salt and chard leaves to pot. Cook chard until water returns to a boil and leaves are tender, about 3 minutes. Using a slotted spoon, transfer chard leaves to ice water. (Keep pot of hot water on stove, but turn off heat.) Drain chard, squeeze out as much water as possible, and chop (you should have about 1/2 cup). Mix chard with ricotta, 1/4 cup parmesan, remaining 1/4 tsp. salt, and pepper to taste. Set aside.
Cut a 5-in.-diameter round from a piece of paper and set aside. Unwrap pasta dough, divide into 6 pieces, and pat each piece into a 1/2-in.-thick rectangle. Working with 1 piece at a time, set a pasta roller on the widest setting and roll piece through, dusting dough with flour as necessary to prevent sticking. Fold piece into thirds (like a letter) and roll it through again. Repeat folding and rolling once more for a total of three rolls on the widest setting. Repeat with remaining 5 pieces of dough.
Set roller to next narrowest setting and roll each piece through once. Repeat with next narrowest setting. Cut each piece in half and roll through on each remaining setting twice, turning 90° between rolls and trimming as necessary to fit and to keep a basically square shape, until dough squares are thin enough to see through and measure at least 5 in. on all sides.
Using paper round as a template, cut 5-in. rounds from each dough square.
Assemble the ravioli: Lay 6 pasta rounds on a clean surface dusted with flour. On each round, use a small spoon to arrange 1/6 of the chard-ricotta mixture in a circle about 3/4 in. from the edges, creating a well in the center large enough to hold an egg yolk. Repeat with remaining 5 pasta rounds and chard mixture. Put an egg yolk in the center of each well. Brush edges of pasta with egg white and place a second pasta round on top of each ravioli. Working from the center of each ravioli, gently press the top pasta round onto the filling to make sure there are no air pockets in the ravioli. Press edges firmly together to seal.
Bring pot of water to a slow boil. With a 4- to 5-in. strainer or slotted spoon, lower ravioli one at a time into the water (cook in batches of 2 or 3). Cook ravioli 3 minutes. Using the strainer, transfer them to a serving plate, blotting excess water with a paper towel. Top each ravioli with 1 tsp. butter.
Sprinkle ravioli with poppy seeds and remaining parmesan. Serve immediately.
Note: Nutritional analysis is per ravioli.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.