Preheat the oven to 400F (204C).
In a large mixing bowl, mix the squash with 5 tablespoons (74 ml) of broth or a drizzle of oil and 1 teaspoon of salt. Place the squash on a parchment-lined cookie sheet and roast for 15 minutes.
Meanwhile, place the apples, leeks, garlic and thyme in the bowl and mix well with the other 3 tablespoons (45 ml) of broth or a drizzle of oil. Add this mixture to the cookie sheet with the roasted squash, mix around to incorporate and roast for 30 minutes.
While the vegetable mixture is roasting, place the rice, pumpkin seeds and the remaining 1 teaspoon of salt into a food processor. Pulse until chopped well.
Once the veggie mix is done roasting, allow it to cool a few minutes, then add the mix to the processor and pulse only a few times to incorporate. Don’t overpulse.
Place the mixture into a bowl, and put it in the fridge for at least 20 minutes; an hour is best. Making this the day before and letting it sit overnight is optimal. This helps all flavors marinate and leads to a sturdier burger.
To cook, shape the mixture into patties. If you’re not using a nonstick pan, then you may want to prepare the pan by brushing it with a tad of oil to avoid sticking. Place the patties in a pan on the stove top over medium heat for 15 minutes on each side. Pans and stove tops vary, so begin to check the patties at 10 minutes. If you try to slide your spatula under a patty and it won’t give, then it isn’t ready and needs to cook longer.
You can also bake the patties on a parchment-lined cookie sheet at 375F (191C) for about 20 to 25 minutes on each side. Allow the patties to cool and set for 5 to 7 minutes. Serve on buns with the Lemon Thyme Mayo and toppings of your choice.

Kids: Make patties into a smaller slider size or into nuggets. Serve mayo on the side as a dipper.