Preheat oven to 400 degrees. Place cherry tomatoes on a foil-lined baking sheet. Drizzle the tomatoes with the oil and season with salt and pepper. Roast the tomatoes for 20 to 25 minutes, until they soften and begin to burst.
While tomatoes are roasting, prepare sauce. In a large saucepan or Dutch oven, melt butter over medium heat and add minced garlic. Cook for 1 minute, stirring frequently, until fragrant. Add the tomato paste and gochujang to the pot. Increase the heat to medium-high and cook the mixture for 3 to 5 minutes, stirring frequently, until the tomato paste and gochujang caramelize. It will begin to brown and stick to the bottom of the pot in places, so reduce the heat if they begin to burn.
Add the heavy cream and chicken broth and bring the sauce to a simmer. Continue simmering, stirring frequently, until the sauce begins to thicken and the tomato paste and gochujang are fully dissolved, 3 to 4 minutes. Reduce the heat to medium-low and stir in the Parmesan and several generous cranks of freshly ground black pepper. Season the sauce with salt to taste and a couple drizzles of honey.
Continue to reduce the sauce until it thickens, about 5 minutes, then gently stir in the roasted tomatoes.
Cook the pasta according to package instructions. Reserve some pasta water to thin the sauce if it seems a little thick.
Drain the pasta, then toss it in the warm sauce and serve immediately with a few more cranks of black pepper and Parmesan Cheese. Garnish with a few sprigs of parsley or basil.