In a medium bowl, combine the beef with the fish sauce, 1 Tbs. of the olive oil, 1/4 tsp. salt, 1/2 tsp. pepper, the sugar, and the chile flakes. Mix well and set aside. Heat a large skillet or frying pan over medium-high heat. Add 2 Tbs. of the olive oil. When the oil is very hot, add the onions and garlic and cook, stirring, until they're slightly golden and fragrant, about 2 minutes. Add the beef and cook, tossing and stirring briskly, until it reaches medium rare, about 1 minute. Remove from the heat.
In a nonreactive bowl, whisk together the vinegar and mustard. Add the remaining 2 Tbs. oil in a slow stream, whisking constantly. Season with 3/4 tsp. salt and 1/4 tsp. pepper. Drizzle the beef with 2 Tbs. of the vinaigrette and toss to combine. Toss the lettuce with the remaining vinaigrette and garnish with the tomato. Lay the beef, onions, and garlic on top of the salad and serve immediately with the white rice.