Pat the flank steak dry and place it in a 9-by-13-inch baking dish. Set aside.
Blend the coconut milk, red curry paste and cilantro stems in a blender on high until fully incorporated and the cilantro stems are very finely chopped. Pour 1 cup of the coconut curry mixture into a large liquid measuring cup and set aside. Pour the remaining mixture over the steak and coat on both sides. Cover the steak and marinate at room temperature for 30 minutes.
Stir 1 1/2 cups water into the reserved 1 cup of coconut curry mixture and transfer to a medium saucepan. Season with 1 teaspoon salt and cook over medium-high heat until boiling. Stir in the rice and bring the mixture to a boil once again. Stir the rice, then reduce the heat to low, cover and cook for 15 minutes.
Heat a grill pan over medium-high heat. Remove the steak from the marinade and drain well on a paper towel-lined sheet pan. Pat the steak with paper towels to remove any excess marinade. Drizzle one side of the steak with about 1 tablespoon oil and use a silicone brush to spread it evenly over the steak. Season with salt and pepper. Transfer the steak to the grill pan, seasoned-side down. Coat the top with about 1 tablespoon oil and season with salt and pepper. For medium rare, grill the steak for 6 minutes per side. Transfer to a rimmed baking sheet and let rest for 10 minutes.
Chop 1/2 cup of the reserved cilantro leaves. Remove the lid from the rice, add the chopped cilantro and fluff with a fork.
Slice the steak against the grain and serve with the rice. Garnish with more chopped cilantro.