Coat a large straight-sided saute pan with olive oil. Add in the red onions, crushed red pepper, and season with salt. Bring the pan to a medium heat and cook the onions until they are soft and aromatic, 7 to 8 minutes.
Add in the squash, dried cranberries, sugar, champagne vinegar, orange zest, mustard seeds, mustard powder, and season with salt. Stir to combine. Add 1 cup of water and bring to a boil and then reduce to a simmer. Cover and simmer for 10 minutes. Remove the lid and cook another 15 minutes, stirring the squash frequently until the liquid has evaporated and the squash is a chutney-like consistency. Check to make sure the squash is cooked through and soft but can still hold its shape. Stir in chives and drizzle with mustard oil.