In a large soup pot over high heat, add one tablespoon of sesame oil. Sear the beef slices on all sides until browned but not fully cooked, about 3-5 minutes. Remove the beef from the pot.
Add the remaining tablespoon of sesame oil to the pot and sauté the onions until tender, about 5-10 minutes.
Add the minced garlic and sauté until fragrant, about 1-2 minutes. Next, add the sliced cherry tomatoes and sauté until they start to release their moisture, about 2-3 minutes.
Deglaze the pot by adding the mirin and rice vinegar. Stir to scrape up any browned bits, then pour in the soy sauce. Stir to combine.
Prepare the broth by stirring the beef and garlic bases into the water. Pour the broth into the pot and bring to a simmer. Continue to simmer for about 5-10 minutes.
While the broth simmers, fry each egg in one tablespoon of butter until the yolk reaches your desired doneness. For a wobbly center, fry for 3-5 minutes; for a hard center, fry for 6-8 minutes.
Stir sriracha into the broth to taste. Add the broccoli florets. If using frozen broccoli, bring the ramen back up to a simmer. If using fresh, allow the florets to simmer for about 3 minutes until bright green. Return the beef to the pot and stir to combine.
Add the udon noodles to the pot. Cook for 2-3 minutes, until the noodles are al dente. Use a ladle to spoon the ramen into serving bowls.
Serve each bowl topped with a fried egg, a squirt of additional sriracha, and optionally, kimchi for added spice. Enjoy!