Bring 1 1/2 cups water to a boil in a small saucepan. Stir in rice, bay leaf, and 1/2 teaspoon salt; cover. Reduce heat to low; simmer 30 minutes. Remove from heat; let stand, covered.
Meanwhile, toast pine nuts in oil in a 10-inch skillet over medium heat. Cook, stirring, until nuts are just browned, about 5 minutes. Transfer nuts with a slotted spoon to a small bowl.
Reduce heat to medium-low; add onions and garlic to skillet. Cook, stirring occasionally, until onions are translucent, about 8 minutes. Add beets and 1 teaspoon salt; season with pepper. Cover; cook, stirring occasionally, until beets are tender, about 25 minutes (if beets stick to skillet, add up to 1/4 cup water).
Remove bay leaf from rice. Stir rice, half of pine nuts, the lemon zest, and parsley into beet mixture. Transfer to a platter. Top with remaining pine nuts and the goat cheese. Garnish with parsley. Serve warm or at room temperature.