Step 1

Heat oil in a large skillet over medium heat. Add onion and cook, stirring often, until soft and translucent but not browned, 7 to 8 minutes. Add chard and spinach, a few handfuls at a time, and cook, stirring often, until wilted, about 5 minutes. Add wine, jalapeño (or serrano), garlic, salt and pepper; cook, stirring occasionally, until the wine is absorbed and the garlic softens, 2 to 4 minutes. Add broth and butter; cook, stirring, until the butter is melted and some of the liquid is absorbed, 1 to 2 minutes.

Step 2

Crack eggs over the vegetables. Cover and cook over medium-low heat until the whites are set, 3 to 5 minutes. Remove from heat and sprinkle with cheese; cover and let stand for 2 minutes before serving.