Place rice in a large bowl and cover with cold water. Agitate using your hand to release excess starch; drain. Repeat process 4 to 5 times until water is mostly clear. Drain and cover with cold water. Let soak at room temperature, uncovered, for 20 minutes. Drain rice well, and set aside.

While rice is soaking, thinly slice white and light green parts of scallions; set aside. Thinly slice dark green parts of scallions to equal ¼ cup; place in a small bowl. Cover using a damp paper towel, and set aside until ready to serve. Reserve remaining dark green parts of scallion for another use.

Heat oil in a medium Dutch oven over medium-high. Add reserved sliced white and light green parts of scallions; cook, stirring occasionally, until softened, about 2 minutes. Add spinach, garlic, salt, and pepper; cook, stirring constantly, until spinach is wilted, about 2 minutes. Add drained rice; cook, stirring constantly, until rice is well coated in oil, about 2 minutes. Add 1 ½ cups water; bring to a boil over high. Reduce heat to maintain a simmer; cover and cook, undisturbed, for 18 minutes. Remove from heat, and let stand, covered, for 10 minutes.

Remove lid from Dutch oven, and stir in dill, mint, butter, and lemon juice. Transfer to individual plates or a platter; top with feta, reserved dark green parts of scallions, lemon zest, dill fronds, and mint leaves. Serve immediately.