For the squash: Preheat the oven to 350 degrees F.
Set the squash on its side. Position a large chef's knife in the ridge between the wedges and use a heavy wooden kitchen spoon to pound it in a bit. Continue to pound and rock the knife blade to get through the tough stem and then split the squash in half lengthwise. Scoop out and discard the seeds. Cut along each rib to make wedges.
Heat 1 tablespoon of the olive oil in a large cast-iron skillet over medium heat. Sprinkle the squash wedges with some salt and pepper and lay them flat in the pan. Sear until golden brown, about 8 minutes. Flip, add the remaining 1 tablespoon oil to the pan, and continue cooking until the second side is deep golden brown, another 8 minutes or so. Transfer the pan to the oven and bake until the wedges are very tender, 15 to 20 minutes. If they are getting too dark, cover them with foil.
For the walnut-parsley pesto: Press out the cloves from the Roasted Garlic heads and add them to a food processor along with the walnuts, parsley and 1/2 teaspoon salt. Pulse until pulverized. With the motor running, drizzle in the walnut oil. Add the Parmesan and some lemon juice, and pulse until just combined.
For the tahini sauce: Whisk together the tahini and lemon juice in a small bowl (it will look thick and slightly dry). Add water, 1 teaspoon at a time, until the sauce is smooth but still thick (it should be pourable). Season with salt and pepper.
To serve, arrange the squash on a platter, drizzle with tahini sauce, spoon over some pesto, and scatter the pomegranate seeds over the top.
Preheat the oven to 350 degrees F.
Cut the tops off the garlic heads, exposing the cloves but leaving the heads intact. Set the heads on a large piece of foil, drizzle with the walnut oil and sprinkle with salt and pepper. Wrap up the foil to make a pouch and place on a baking sheet. Bake until the garlic is soft and roasted, 35 to 40 minutes. Set aside to cool.