Bring the steak to room temperature if possible, then preheat a large skillet or grill pan over high heat until very hot.
Lightly oil the pan with a small amount of cooking oil to prevent sticking.
Sear the steak on the hot pan for about 1 minute without moving to form a crust, then flip and sear the other side for about 1 minute.
Reduce heat to medium and continue cooking until the steak reaches your desired doneness (time will vary by thickness).
Remove the steak, wrap it loosely in aluminum foil, and rest for 5–10 minutes, then thinly slice across the grain.
While the steak rests, make the dressing: whisk together the fish sauce, lime juice, chopped bird's eye chilies, and sugar to taste in a mixing bowl.
Add the mint, cilantro, thinly sliced shallots, and halved cherry tomatoes to the dressing and toss to combine.
Arrange the spinach on a serving platter or plates, top with the sliced steak, then spoon the herb-and-shallot mixture over the steak and spinach. Drizzle with extra dressing as desired and serve.