For the chocolate BBQ sauce: Heat the oil over medium-high heat in a medium heavy-bottomed saucepan. Add the onion and garlic and cook, stirring once or twice, until soft, 3 to 4 minutes. Add the ketchup, beer, brown sugar, molasses, mustard, vinegar, Worcestershire sauce, chipotle chile and some salt and pepper and whisk until smooth. Whisk in the ancho powder, cocoa powder, paprika and chile de arbol. Bring to a simmer and cook, stirring occasionally, until thickened, about 20 minutes. Stir in the chopped chocolate and cook, stirring occasionally, another 5 minutes.
Transfer the mixture to a food processor and puree until smooth; season with salt and pepper to taste. Pour into a bowl and allow to cool to room temperature. The sauce will keep for 1 week in the refrigerator stored in a tightly-sealed container.
For the steak: Stir together the ancho powder, cocoa powder, salt, espresso, celery seed, coriander, oregano, paprika, allspice, mustard seed and black pepper in a small bowl.
Remove the steak from the refrigerator 20 minutes before cooking. Season the steak on both sides with salt and pepper. Rub one side with some of the rub. Store the remaining rub in an airtight container in a cool dark place for up to 2 months.
Heat the canola oil in a cast-iron pan over high heat until it begins to shimmer. Add the steak rub-side down and cook until a crust forms, about 4 minutes. Turn over, reduce the heat to medium, and continue cooking, brushing with the chocolate BBQ sauce every few minutes, until the bottom is golden brown and the steak is cooked to medium-rare, 4 to 5 more minutes. Remove to a cutting board, brush with more of the sauce and let rest 10 minutes. Slice into thick slices.
For the cheesy green eggs: Crack the eggs into a large bowl and whisk until light and fluffy. Melt the butter in a large nonstick skillet over medium heat. Add the eggs and cook, stirring constantly, until soft curds form. Just before the eggs are softly set, stir in some salt and pepper and the Cheddar. Remove from the heat and stir in the cilantro and green onions.
For the burritos: Spread each tortilla with some sour cream. Add some chocolate BBQ sauce, cheesy green eggs, steak, salt and pepper, and more sauce if desired. Roll up into burritos and serve with additional eggs, sauce and steak on the side if desired.