Make the Chipotle Crema:
In a blender, combine all chipotle crema ingredients and puree until smooth. Taste and adjust seasoning with more salt or spice as needed. Set aside.
Make the Nacho Cheese:
In a medium saucepan over medium-low heat, melt butter. Whisk in flour until smooth and cook for 1-2 minutes. Gradually add the warm milk and whisk until fully combined. Remove from heat, stir in the cheeses until melted, then add jalapeño juice, cayenne, and salt to taste. Set aside.
Make the Taco Beef:
In a large skillet, heat oil over medium-high. Add beef in large chunks and press down to brown. Flip and brown all sides, then break into small pieces. Add taco seasoning and follow packet instructions to finish.
Make the Cilantro Lime Rice:
Toss warm rice with butter, lime juice, lime zest, and fresh cilantro.
Assemble, Wrap, and Bake:
Spread nacho cheese on one tortilla, leaving 1/2 inch around the edges. Top with shredded cheese, then add another tortilla. In the center-lower third of each tortilla, add cilantro lime rice, taco meat, more nacho cheese, chipotle crema, Greek yogurt, and cilantro. Carefully roll into a burrito, sealing the sides.
Bake, Sear, and Serve:
Preheat the oven to 350°F and arrange a rack in the center. Wrap each burrito in parchment paper, place on a baking sheet, and bake for 15 minutes. Remove from the oven and sear in a skillet over medium heat until golden brown on both sides. Serve immediately with extra chipotle crema and Greek yogurt.