Preheat the oven to 350°F. Spread the cornbread in a single layer on a large rimmed baking sheet. Bake until dry and beginning to brown, about 25 minutes. Cool.
Meanwhile, butter a small rimmed baking sheet. Melt 1½ tablespoons butter in a large nonstick skillet over medium heat. Add the cumin and stir until fragrant, about 30 seconds. Remove the skillet from the heat, add the cayenne and then the pecans, sugar, and ¼ teaspoon salt. Stir to coat the nuts. Transfer to the prepared baking sheet. Bake until the pecans begin to brown, about 6 minutes.
Heat 2 tablespoons of the oil in a large nonstick skillet over medium-high heat. Add the sausage and sauté until starting to brown, about 4 minutes. Transfer the sausage to a large bowl, leaving any drippings in the skillet. Add the remaining 1 tablespoon oil, celery, onion, and bell pepper. Sprinkle with salt and black pepper and sauté until the onion begins to brown, about 10 minutes. Add to the bowl with the sausage. (Can be prepared 1 day ahead. Store the bread and pecans airtight at room temperature. Cover the sausage-vegetable mixture and refrigerate. Bring the sausage-vegetable mixture to room temperature before continuing.)
Preheat the oven to 350°F. Brush olive oil over a 2-quart casserole or 13x9x2-inch glass baking dish. Add the cornbread cubes, pecans, marjoram, and some freshly ground black pepper to the vegetable-sausage mixture and toss gently to combine. Whisk the broth and egg together in a small bowl. Add to the cornbread mixture and mix gently. Transfer the stuffing to the prepared dish. Bake uncovered until crisp and brown on top about 45 minutes. Let cool 15 minutes before serving.