Preheat oven to broil
In a small bowl combine half the soy sauce, half the brown sugar, ½ teaspoon salt and ½ teaspoon black pepper. Rub mixture over steak and set aside until needed.
Line a baking sheet with foil and set aside
Zest half the lime and cut in half.
In a small saucepan over high heat, bring 1/1/4 cups water and ¼ teaspoon salt to a boil. Stir in rice and return to a boil. Reduce heat to low, cover and simmer for 15 minutes. Turn off heat and let sit, covered for 5 minutes. Fluff with a fork and gently stir in sesame oil, lime zest, the juice from half of a lime and all but 1 tablespoon of the scallions.
While cooking rice, place pineapple spears in a single layer on the foil-lined baking sheet and brush tops with 1 teaspoon oil. Lightly sprinkle spears with salt. Broil until charred in places (about 15 minutes)
Remove pineapple from oven and sprinkle with the remaining brown sugar and red pepper flakes to taste.
Rub a grill pan (or grill outdoors) with 1 teaspoon cooking oil and place over high heat. When the grill pan starts to smoke, add steaks and cook to medium-rare (or your preference), turning once. Cook each side 3-4 minutes or as needed to the desired temperature. Remove to a plate and allow to rest for 5 minutes. Thinly slice steaks against the grain.