Rinse the lentils and set them in a 4-quart Dutch oven with the bay leaf and enough water to cover by 5 cm / 2 inches. Bring to a boil, then reduce heat and simmer for 15 minutes, until just tender but not falling apart. Drain and set aside, discarding the bay leaf.
While the lentils cook, heat 3 tbsp olive oil in a 12-inch skillet over medium heat. Add the sliced topping onions in two batches so they have room to spread out, cooking each batch 20 to 25 minutes, stirring occasionally, until deep amber brown. Season with 1/4 tsp salt and transfer to a paper towel-lined plate.
In the same Dutch oven, heat the remaining 3 tbsp olive oil over medium heat. Add the diced onions and cook for 8 to 10 minutes, until soft and golden.
Stir in the garlic, cumin, coriander, cinnamon, and black pepper. Cook for 1 minute, until fragrant.
Add the rinsed rice, drained lentils, broth, and 1 tsp salt. Stir once, bring to a boil, then cover and reduce heat to low. Simmer for 18 to 20 minutes, until the rice is tender and the liquid is absorbed.
Turn off the heat and let the pot sit, covered, for 10 minutes so the rice finishes steaming.
Fluff the lentils and rice with a fork. Taste and add more salt if needed.
Pile the mujadara onto a platter, top with the crispy onions, and scatter parsley or mint over the top. Serve warm with lemon wedges on the side.