Polenta-Stuffed Kabocha Squash

Preheat oven to 400 degrees F.

Using a small sharp knife and working at a slight angle, cut a 3-inch circle off the top of each squash. Scoop out the seeds. Rub the flesh and skin of each squash with 1 tablespoon oil. Scatter garlic inside.

Roast the squash in a baking pan until the flesh is tender but the sides are not yet collapsing, 30 to 40 minutes.

Meanwhile, heat butter and the remaining 2 tablespoons oil in a large saucepan over medium-high heat. Add onions, 1/4 cup sage and thyme; cook, stirring often, until the onions are just starting to brown, 5 to 7 minutes. Season with salt and pepper. Add cornmeal, then whisk in broth. Bring to a gentle boil. Reduce heat, cover and simmer, whisking frequently, until the cornmeal is tender, 10 to 15 minutes.

When cool enough to handle, scrape about 1 cup of flesh out of each squash, leaving a layer in the shell so it retains its shape. Mash the flesh into a coarse puree and add to the polenta along with Carmody (or havarti) and Parmesan cheeses; stir well. Spoon into the squash shells.

Bake the stuffed squash until the cheese is melted and the polenta is steaming hot, about 20 minutes. Serve garnished with sage, if desired.