In a large pot, combine the chicken broth and water. Bring to a boil over medium-high heat.
Once boiling, add the ramen noodles and cook according to package instructions, usually about 3-4 minutes. Stir occasionally to prevent sticking.
In a skillet, heat the vegetable oil over medium heat. Add the shredded chicken, soy sauce, chili paste, and sesame oil. Stir and cook for about 5 minutes, letting the chicken absorb the flavors. Set aside.
In the same skillet, melt the butter. Add the minced garlic and sauté for 1-2 minutes until fragrant, avoiding burning.
Stir in the heavy cream and soy sauce. Bring to a simmer, then mix in the cornstarch dissolved in water to thicken the sauce. Season with salt and pepper. Cook for another 2-3 minutes.
While the sauce simmers, soft boil the eggs in boiling water for 6-7 minutes. After cooking, transfer them to ice water to cool for easy peeling.
Once the ramen noodles are cooked, drain them and divide them among four serving bowls. Top each with the spicy chicken mixture and pour the creamy garlic sauce over the top.
Slice the soft-boiled eggs in half and add them to each bowl. Garnish with sliced green onions.