Hearty sweet potatoes and chickpeas create a burger that's about as meaty as it gets without using any meat. Dried chickpeas keep these patties crispy; soak them overnight so they're ready to cook when you are.
In a bowl, soak chickpeas in 4 cups water for at least 12 hours and up to 24; drain well.
Heat oven to 375°. Coat a baking sheet with cooking spray. In a food processor, process chickpeas, tahini, black pepper, baking powder and 3/4 tsp salt, scraping down sides as necessary, until mixture holds together when pinched, 2 minutes; transfer to a bowl. Stir in sweet potato.
In a second bowl, combine cucumber, onion, dill, vinegar and remaining 1/4 tsp salt; set aside.
Form chickpea–sweet potato mixture into 4 burgers; place on baking sheet; cover tightly with foil; bake 20 minutes.
Remove foil; coat burgers with spray; bake until crisp and golden underneath, 20 to 25 minutes.
Flip burgers; coat with cooking spray; bake until crisp on other side, 10 to 15 minutes. Serve burgers with dilly cucumbers.