Split the cucumber in half with a knife. Heat a heavy bottom sauté pan on high heat. Put in 1 tsp. of the canola oil, and using a paper towel, wipe the oil leaving just a thin layer. The pan should be smoking hot. Place the cucumber flat side down and press down with a metal spatula leaving the pan on high heat. Once the cucumber has a good char on the flat side, remove it from the pan and place on the cutting board to cool. Clean the sauté pan to cook the peppers.
Cut the red bell pepper in half, remove the stem, seeds, and ribs. Cut the bell pepper into ½” strips. In the large sauté pan on high heat, add in 2 tbsp. of canola oil and let the oil heat to smoking. Carefully add in the peppers and leave on high heat. Continue to cook until the peppers are soft and have a good char but not completely burnt. Moderate the pan heat as needed. Line a plate with a paper towel and lay out the peppers on the plate to cool.
Once the cucumber is cooled, cut it into half-moon shapes about ½” thick. Add to the peppers and keep aside.
In a medium-large saucepot, bring 2 quarts of water to a rolling boil. Add the instant noodles and stir to make sure they cook evenly. Cook the noodles for about 2-3 minutes. Test a noodle to make sure it is al dente. Drain the cooked noodles into a colander.
In the same pot add in the 1 ½ cups of unsalted beef broth. Turn on medium heat. Add in the black bean-seasoning packet from the Chapagetti and only half of the seasoning powder from the neoguri package. If you like it spicy, add the whole pack from the Neoguri package. Bring the sauce to a boil.
Add in the meatballs and cook for 2 minutes to warm them through.
Add in the cooked noodles to the pot of meatballs and sauce. Continue to simmer to reduce the sauce and coat the noodles and meatballs, stirring often with a rubber spatula.
Add in the cut charred cucumber and peppers and fold in the noodles with a rubber spatula. Add in the oil pack from the Chapagetti at the end and fold together. Finish by folding in the thinly sliced scallions, reserving some to place on top.
Place the noodles into four bowls with the meatballs. Put some of the sliced scallions on top. Serve with the lime wedge on the side and kkakdugi radish banchan. Serve immediately