Put the oil in a large skillet over medium-high heat. When it's hot, add the squash and cook, turning occasionally, until they're soft and beginning to brown on the edges, about 10 minutes. Add the spinach and cook, stirring frequently, until it's just wilted, about 2 minutes more; set aside.
In a medium saucepan, add the cornmeal along with 1 cup water and whisk well to make a slurry; continue whisking to eliminate any lumps. Place the pan over medium-high heat, sprinkle with salt, and bring to a boil. Reduce the heat to medium and continue to cook, whisking frequently and adding water as needed to keep the polenta smooth and free of lumps (this will take between 3 and 4 more cups of water depending on the grind of your polenta). Cook until the polenta is tender and creamy, 15 to 30 minutes. If the mixture becomes too thick, add a bit more water to thin it; you're looking for a consistency similar to sour cream.
Add the butter and taste; season with salt if necessary, and sprinkle with lots of pepper. Spoon the polenta into serving bowls and top with vegetables. Makes 4 servings.