Preheat the oven to 425˚. Combine the onion, sweet potatoes, 1/4 cup olive oil, 1/2 teaspoon salt and a few grinds of pepper in a medium ovenproof nonstick skillet. Cover and cook over medium-high heat, stirring occasionally, until the sweet potatoes are tender but not falling apart, 6 to 8 minutes.
Whisk the eggs in a large bowl and season with salt. Pour the potato mixture into the eggs and stir to combine. Stir in the cheese. Place the skillet over medium heat; add the egg mixture and spread out the potatoes with a rubber spatula. Cook until starting to set around the edges, 1 to 2 minutes. Transfer the skillet to the oven and bake until set, 12 to 15 minutes.
Meanwhile, whisk the vinegar and mustard in a large bowl; whisk in the remaining 2 tablespoons olive oil until smooth. Add the endive, almonds and 2 tablespoons chives; toss and season with salt and pepper.
Remove the egg tortilla to a cutting board, cut into wedges and divide among plates. Sprinkle with the remaining 1 tablespoon chives and serve with the endive salad.