Step 1
Preheat oven to450º and line a large baking sheet with foil. Rinse tomatillos well, then cut in quarters. On prepared baking sheet toss with ½ tablespoon oil and season with salt. Roast until tomatillos are softened and starting to char slightly, 20 minutes, turning halfway through. Remove from oven and reduce heat to 325º.
Step 2
Cook Swiss chard: Meanwhile, strip chard leaves from stems, reserving half the stems. Working in batches, finely chop the leaves by stacking 4to 5 leaves and rolling them tightly. Thinly slice the roll vertically, then finely chop the strips of leaves. Finely chop stems, keeping them separate from chard leaves.
Step 3
In a large ovenproof skillet over medium heat, heat 2 tablespoons oil. Cook chard stems, onion, and jalapeño, if using, until softened and golden, 5 to 7 minutes. Add garlic and cook until fragrant, 1 minute.
Step 4
Working in batches, add chopped chard leaves to skillet, allowing each batch of greens to cook down and reduce slightly before adding more. Cook greens for 5 minutes, or until fully wilted. Season with salt and pepper.
Step 5
Blend sauce: While the greens cook, add roasted tomatillos, herbs, remaining 1 tablespoon oil, and 1 cup water to a blender. Blend until smooth, then add sauce to the chard mixture.
Step 6
Bring sauce to a slight boil, then reduce heat and bring to a simmer. Use a wooden spoon to create 6 evenly spaced wells in the simmering sauce. Carefully crack an egg into each well and season each with a sprinkle of salt and pepper. Remove pan from heat and transfer to oven.
Step 7
Bake eggs: Bake until eggs are just set and yolks are still runny, 10 to 13 minutes.
Step 8
Garnish with avocado slices, cheese, and cilantro, and serve with warm corn tortillas or crusty bread.