Heat avocado oil in a large pot over medium-high heat. Add the shallot and cook for 5 minutes until it just begins to soften.
Add the capers and cook 1 minute. Add crushed red pepper and cook for 30 seconds.
Toast the rice:
Melt the butter into the pot. Add the rice and cook for 2 minutes. Season with salt. Add the water and bring to a boil. Reduce heat, cover, and simmer for 20-25 minutes until the rice is tender and the liquid is absorbed.
Cook the zucchini:
Meanwhile, prepare the zucchini. Arrange the zucchini on a sheet pan and drizzle with extra virgin olive oil. Flip the zucchini ensuring both sides are coated with oil. Season the zucchini on both sides with salt and pepper. Transfer to the oven for 15-20 minutes until golden brown, flipping once midway through cooking.
Finish the zucchini:
Remove the zucchini from the oven and sprinkle all but a pinch of the parmesan on the zucchini. Broil for 2-3 minutes until the cheese is melted and the tops are golden brown. Set aside.
Finish the rice:
Remove the rice from the heat and stir in the chickpeas, dill, and lemon juice. Season all over with salt. Cover and let stand for 5-6 minutes.
To serve:
Divide the rice and chickpeas between plates and arrange the zucchini on top. Garnish with more parmesan and dill, if desired. Enjoy!