Place the uncooked tteokbokki in a medium bowl. Add cold water to the bowl until the tteokbokki is submerged. Set aside.
Thinly slice the green onions, reserving a handful of the green section for topping. Cut the ginger into thin strips, then finely chop the garlic.
Place a large pan over medium heat. Add the olive oil. Once hot add the green onions. Cook for 1-2 minutes. Add the ginger and garlic and cook an additional minute.
Add the sausage. Use a spoon to break it into smaller pieces, then stir as it continues to cook.
Once the meat is almost cooked through, add the broccoli or green beans. If using green beans, cut them into 2-inch chunks before adding. Stir as the vegetables cook for 2-3 minutes.
Chop the curry block into smaller pieces. Scrape everything in the pan to one side. Place the curry blocks in the empty side of the pan. Add 1 cup of water and stir as the curry blocks dissolve. Once dissolved, stir the sauce into the rest of the mixture. If the sauce is too thick, add more water. It will continue to thicken, so it’s okay for it to be quite runny at this point.
Drain the water from the tteokbokki. Add the tteokbokki to the pan and stir to combine. Place a lid on the pan and let it simmer for 3-4 minutes. Once the tteokbokki is soft and chewy and the sauce has thickened, turn off the heat. Add the sesame oil and stir to combine.
Divide into bowls and top with cilantro and the reserved green onions. Enjoy!