Start by preparing the tofu. Preheat your oven to 425 F and line a baking sheet with parchment.
Cut your tofu into cubes and line on the baking sheet. Toss with salt, pepper, and crushed red pepper (if desired) and bake for 25-30 minutes, flipping halfway through.
While the tofu is baking, prepare the sauce. Mix all of the sauce ingredients together in a small bowl, until fully combined. Depending on the thickness of your tahini, you may require more coconut milk to thin it out. I use a rather liquidy tahini, but if yours is thicker, you can add in milk 1 tsp at a time until it reaches your desired consistency.
Next, prepare the vegetables. Remove the ends from your green beans and chop in half. Set aside in a small bowl. Peel your carrot into ribbons and place them in another bowl. Finally, prepare your shiitake mushrooms by removing the stems and chopping the caps in half (note: you can discard the stems or fry them in a little butter at the very end!)
Heat a pan on the stove and melt the butter, being careful not to brown it. Add in your onion, green beans, and mushrooms, and cook for about 3 minutes, moving constantly. Cover with the lid, and cook for another 2 minutes.
Next, add in the carrots and cook for another 2-3 minutes.
Once your vegetables are fully cooked, season generously with salt, pepper, and gochujang. You can vary the amount of gochujang depending on your spice preference.
Finally, prepare your noodles according to the package; udon noodles cook fairly quickly, within 2-3 minutes. Once cooked, strain the water from them and add them to the pan with the vegetables.
Add your tofu to the pan and then pour the sauce over the noodles, veggies, and tofu, making sure everything is evenly coated.
Garnish with green onion and sesame seeds, and enjoy!