Preheat the oven to 400℉ and line a baking sheet with parchment paper. Split the honeynut squash lengthwise down the centre and scoop out the seeds. Transfer the squash to the baking sheet, drizzle it with olive oil, and season with sea salt and fresh black pepper. Turn the squash so the cut side is facing down. Peel the garlic cloves, place them on a piece of aluminium foil, and drizzle with olive oil. Wrap up the cloves and add them to the baking sheet with the squash. Roast for 40 minutes, rotating the pan after 20 minutes.
While the squash is roasting, prepare the mushrooms. Roughly chop the oyster mushrooms into bite-size pieces. Thinly slice the shallot and mince the fresh sage. Heat a large pan over medium heat, then add the chopped mushrooms.
Cook the mushrooms in the dry pan, stirring occasionally, to draw out the water content. Once most of the water has evaporated and the pan is dry, add 1 tablespoon of olive oil, the sliced shallots, and the sage. It will take about 10 minutes to get the moisture out of the mushrooms in the dry pan.
Cook the mushrooms, shallots, and sage, stirring frequently, for about 20 minutes. Both the mushrooms and shallots should be nice and soft. Season with sea salt and fresh black pepper, to taste.
Once the squash is fork-tender, remove it from the oven. Flip the squash over so the cut side is now facing up. Let the squash rest until cool enough to handle.
Bring a large pot of heavily salted water to a boil and cook the rigatoni noodles according to package instructions. Save about 1 cup of pasta water to thin out the honeynut and ricotta sauce.
Scoop out the cooled squash flesh and transfer it to a high-speed blender along with the roasted garlic cloves and ricotta cheese. Blend until completely smooth, season with sea salt and fresh pepper, then pulse again.
Drain the noodles and add them to the pan with the mushrooms. Pour over the pureed honeynut squash ricotta sauce, stirring to coat the noodles. Add the reserved pasta cooking water bit by bit until the desired consistency is achieved. Taste and adjust the seasoning as needed. Serve immediately with lots of parmesan cheese and fresh black pepper.