Heat a large sauté pan or paella pan, coated with olive oil,over medium-high heat. Brownthe vegetables in batches andsauté until they are caramelized. First the squash, carrots, and parsnips, set aside while cooking mushrooms, peppers and eggplant with garlic.
Once all the vegetables are browned, add them all back to the pan; add the wine, saffron, rice, water, and sofrito. Stir tocombine. Cook the mixture over medium heat until the rice begins to swell.
Add the remaining ingredients but do not stir them in. Continue to cook until the rice is tender.
Turn off the heat and cover the paella with a towel, allowing it to sit before serving so the flavors can meld. Pass garlicky allioli.