Preheat the oven to 425°F and set a rack near the bottom. Place the whole honeynut squash on a sheet pan and roast for 30 minutes or until softened. Take out of the oven and set aside to cool. Turn off the oven. When the squash is cool, remove the seeds and skin and set the purée to the side.
While the squash is roasting, soak the frozen tteokbokki in a large bowl of water. Set aside.
Drain the tofu and press out any moisture. Cut it into 1-inch pieces.
Set a large pan or braising dish (at least 3.5 quart size) over medium heat. Add 1 tablespoon of butter and 1 tablespoon of olive oil and let the butter melt, then sear the tofu for 4-5 minutes on each side or until golden and crisp. Remove the tofu from the pan and set aside.
If you are making the seed topping, add another tablespoon of butter, the pumpkin seeds, peanuts, gochugaru and ½ teaspoon of salt. Toast for 2-3 minutes, then add 2 tablespoons of thinly sliced scallion greens. Toast another minute until everything is fried and golden, then remove from the pan and set aside.
Add another 2 tablespoons of olive oil to the pan. Cook the scallions and garlic for 2-3 minutes, then add the softened interior of the honeynut squash and 1 heaping tablespoon of gochujang. Pour in 2 cups of water and bring to a simmer. Mix until smooth, then taste and season with salt as needed, I use about 1 teaspoon.
Add the tteok and bring to a simmer for about 8-10 minutes. It should go from a thin sauce to glossy.
Add the tofu back in. Stir in 3 cups of your greens of choice.
Serve warm, topping each portion with a sprinkling of the gochugaru nuts.
