In a pot on medium-high heat, soften the onions in oil. With a garlic-press, add the garlic and ginger directly to the pot to get all the juices. Add the rice and stir until well combined.
Add the potatoes and the squash, the vegetable broth and the bay leaves. Bring to a boil.
Reduce heat, add the zucchini, cover and let simmer until the vegetables are tender and the rice is cooked, between 20 to 30 minutes. Add broth if necessary.