Heat the cooking oil in a pan or pot over medium heat. Add the minced garlic and cook until fragrant and just beginning to brown.
Add 2 tablespoons of butter along with the oregano, thyme, and paprika. Once the butter has melted, stir in the flour and cook for about 1 minute.
Pour in the vegetable broth first and stir until combined. Add the whole milk, followed by the drained and rinsed butter beans. Season with salt and black pepper to taste.
Lower the heat to medium-low and simmer for 8–10 minutes, stirring as needed. Some of the butter beans will begin to break down slightly as the sauce develops more body. Once the sauce begins to lightly stick to the bottom of the pan, it has reached the consistency you’re looking for.
Turn off the heat. Stir in the heavy cream, sliced sun-dried tomatoes, and remaining 2 tablespoons of cold butter. Stir until the butter has melted and the sauce is smooth and glossy.
Serve the Marry Me butter beans with a generous amount of freshly grated Parmesan and chopped fresh basil over the top.