Heat a large heavy-bottomed pot over medium heat and add olive oil. Add the diced onion and sauté until it becomes translucent and fragrant, about 5 minutes.
Add the minced garlic and cook for another minute, stirring until fragrant, being careful not to burn it.
Toss in the cubed squash, sliced carrots, and cubed sweet potato. Stir well to coat the vegetables with the oil and cook for about 7-8 minutes, allowing them to start softening and develop some color.
Pour in the vegetable broth, bringing the mixture to a gentle simmer. Cover the pot partially and cook for 20-25 minutes, or until the vegetables are tender and easily pierced with a fork.
Uncover the pot and stir in the smoked paprika, along with salt and pepper to taste. Allow the stew to simmer uncovered for another 5 minutes, letting the flavors meld and the broth slightly reduce.
Add the chopped kale and cook until it wilts and turns a vibrant green, about 3-4 minutes, stirring occasionally.
Taste and adjust seasonings with more salt, pepper, or smoked paprika if desired. Serve the stew hot, with a hearty spoonful ready to enjoy.