Put a large frying pan over medium high heat and add a little oil and the pork. Season with salt and pepper. Cook on medium high heat for about 8 minutes to brown and break up. Transfer to a bowl. Keep some of the fat in the pan and discard excess fat if needed.
Add the potato and onion to the pan and continue to cook on medium high, stirring occasionally, Season with a little salt but use caution because there are salty ingredients in the sauce. Cook about 10 minutes until browning on the edges.
Add the zucchini and radish and cook another 6-8 minutes until all the veggies have reduced in size, softened, and lightly browned.
Add in the garlic and ginger along with 1 tablespoon of the sesame oil and the gochugaru. Cook 3 minutes. Add the pork back in and stir to combine.
Add in the tomato and bean pastes and cook 3 minutes, stirring the pastes into the veggies and meat.
Add in the water and bring to a simmer. Turn to low. Cook about 10 minutes.
At this point, you can also put on a pot of heavily salted water for the pasta.
Cook the pasta to package instructions. Just before straining the pasta, reserve 1/2 cup of the pasta cooking water.
Remove the sauce from the heat and stir in the remaining sesame oil as well as the soy sauce.
Strain the pasta and quickly pour the sauce over it. Add the reserved pasta cooking liquid. Stir to combine the pasta and the sauce.
Serve the pasta and top with sliced cucumbers and gochugaru.