Step 1Heat a large, nonstick skillet over medium heat. Place the tortilla in the skillet and warm, flipping once, until pliable, about 30 seconds. Transfer to a cutting board or plate larger than the skillet.
Step 2Raise the heat to medium-high. Pour the oil into the pan and swirl to coat. When it shimmers, add the tomato in a single layer. Sprinkle with the sugar and a pinch of salt. Stir once and let sear until caramelized on the bottom, about 2 minutes. Add the avocado, sprinkle with salt, and sear until lightly browned, about 1 minute.
Step 3Crack the eggs into the pan and immediately stir vigorously to scramble, then gently stir to distribute the egg-tomato-avocado in an even round smaller in diameter than the tortilla. Season with salt and sprinkle the cheese on top, then center the tortilla over the mixture and press gently. There should be a 1 to 2 inch rim between the tortilla and filling. Let stand until the cheese melts against the tortilla, about 2 minutes.
Step 4Remove from heat, then quickly flip the tortilla with the filling clinging to it onto a cutting board or plate. (To ensure nothing spills, you can center the board or plate over the skillet and carefully flip both together, then lift off the skillet.) Fold in two sides of the tortilla, then roll tightly so the filing is spiraled with the tortilla. Immediately wrap in foil and eat, adding salsa or hot sauce if desired.