Melt the 3 tablespoons butter in a large saucepan over medium-high heat.
Add the diced onion and minced garlic; cook 3 to 5 minutes until tender. Softening them first draws out sweetness before any liquid goes in.
Stir in the curry powder, salt, ground coriander, and crushed red pepper; cook 1 minute. Blooming the spices in fat is what carries their flavor through the whole pot rather than leaving it flat on top.
Pour in the 4 cups stock and add the corn kernels, hominy, and white beans; bring to a boil.
Reduce heat to low and cook, stirring occasionally, 15 to 20 minutes to develop the flavors.
Stir in the pureed squash and cook 5 minutes, until heated through. Adding it late keeps the puree from scorching on the bottom during the long simmer.
Serve warm, garnished with chives and plain yogurt.