Bring a small pot of water to a boil. Gently lower in the eggs and boil for exactly 6 1/2 minutes. Transfer to an ice bath, cool for at least 2 minutes, then peel and set aside.

Bring a separate pot of water to a boil. Add the ramen noodles and cook for 2 minutes, 1 minute less than the package says. Drain and set aside.

Melt the butter in a large skillet over medium heat. Add the garlic and ginger and cook for 1 minute, stirring constantly, until fragrant but not browned.

Pour in the broth, cream, soy sauce, brown sugar, and sriracha. Whisk and bring to a simmer for 3 to 4 minutes, until thickened enough to coat a spoon. Remove from heat and whisk in the Parmesan until melted. Season with black pepper.

Add the noodles to the skillet and toss until fully coated. Divide between bowls, top with halved soft-boiled eggs, green onions, and sesame seeds. Serve immediately.