Preheat the oven to 400°F. Line a baking sheet with parchment paper.
Toss the butternut squash cubes in 1 tablespoon of the olive oil. Arrange them on a baking sheet and bake for 20-25 minutes, until tender and lightly browned. Leave the oven on when you remove the baking sheet.
Place a large skillet over medium heat and add 1 tablespoon of olive oil. Let the oil heat up for a minute, then add the onion. Cook the onion for about 5 minutes, until it starts to soften, stirring occasionally.
Add the garlic and cumin. Cook the mixture for about 1 minute, stirring constantly, until very fragrant.
Stir in the butternut squash, black beans, chipotle peppers, adobo sauce, and water. Raise the heat to high and bring the mixture to a boil, then reduce the heat and let the mixture simmer for about 5 minutes, stirring occasionally, until most of the liquid has evaporated.
Remove the skillet from heat, then stir in the cilantro, lime juice, salt, and pepper. Taste the mixture and adjust any seasonings to your liking.
Place a fresh sheet of parchment paper on your baking sheet. Arrange a tortilla on a work surface, then spoon a fifth of the filling (about ⅔ cup) in the center. Fold the side closest to you over the filling, tuck in the sides, then roll the tortilla away from you. Place it on the baking sheet, seam side down. Repeat the rolling process for the remaining tortillas and filling.
Brush all sides of the unbaked chimichangas with the remaining 2 tablespoons of olive oil, then place them back on the baking sheet with the seam sides down.
Bake for about 20 minutes (oven should still be at 400°F), until the tortillas begin to crisp and lightly brown.
Serve with toppings of choice, and enjoy!