Preheat the oven to 400 F. Line a sheet pan with parchment.
Slice the squash in half, vertically, then scoop out the seeds. Slice into thin wedges, then either slice off the skins (see video) or leave the skins on. Place on the prepared pan and drizzle with a little avocado oil, toss and spread on the pan.
Roast for 20 minute, until tender and browned. Cool on a rack.
For the sauce, place the stock, maple, vinegar, soy sauce, sesame seeds, ginger and garlic in the blender, and secure the lid. Grind until smooth, scraping down as needed.
Transfer the sesame mixture to a small pan, then heat over medium-high, stirring. Add water as needed as you stir and bring to a boil.
Arrange arugala on plates, then compose the squash claws on top, then drizzle with sesame sauce.