Preheat the oven to 350 degrees F and line a sheet pan with parchment paper.
Toss butternut squash and onions with 1 tablespoon olive oil, then spread out on to the sheet pan in an even layer. Bake for 15 minutes, or until just starting to soften. Let cool.
In a large bowl, combine the chick pea flour, corn starch, baking powder, salt and pepper, then mix to combine. Add the butternut squash and onions, the egg and ¼ cup water. Mix until it forms a tight batter and everything is thoroughly combined.
Heat the remaining 3 tablespoons of olive oil in a large skillet over medium-high heat. Use a ¼ cup measuring cup to scoop out the batter (don't fill it all the way) and place it in the pan. Use the back of the cup to flatten it just a bit, then repeat 3-4 more times, but don't overcrowd the pan. When they're starting to brown on the outsides, give them a flip and cook until browned on the other side. Repeat until you've used up all the batter.
Transfer fritters to a baking rack set over a sheet pan to drain. Sprinkle with flaky sea salt, then pop the pan in the oven (still set to 350 degrees F) while you make the spiced yogurt.
In a small bowl, add the yogurt, garlic, cumin, coriander, smoked paprika, salt and lime juice. Whisk until thoroughly combined, then transfer to a serving bowl.
Remove the fritters from the oven, transfer to a platter, then serve immediately with spiced yogurt on the side.