Fill a medium pot 3/4 of the way up with salted water; cover and heat to boiling on high. Wash and dry the fresh produce. Medium dice the potatoes. Peel and roughly chop 2 cloves of garlic (or 4 cloves for 4 servings). Cut off and discard any stem ends from the green beans. In a bowl, whisk together the sugar, 1/4 cup of water (or 1/2 cup for 4 servings), and as much of the chile paste as you'd like, depending on how spicy you'd like the dish to be.

Add the diced potatoes and half the chopped garlic to the pot of boiling water. Cook 16 to 20 minutes, or until tender when pierced with a fork. Turn off the heat. Drain thoroughly and return to the pot. Add the buttermilk and 2 teaspoons of olive oil (or 4 teaspoons for 4 servings); season with salt and pepper. Using a fork or potato masher, mash to your desired consistency. Taste, then season with salt and pepper if desired. Cover to keep warm.

Meanwhile, in a medium nonstick pan (or large for 4 servings), heat a drizzle of olive oil on medium-high until hot. Add the green beans in an even layer. Cook, without stirring, 2 to 3 minutes, or until lightly browned. Season with salt and pepper. Carefully add the remaining chopped garlic and 2 tablespoons of water (or 4 tablespoons for 4 servings). Cook, stirring occasionally, 2 to 3 minutes, or until the green beans are softened and the water has cooked off. Transfer to a bowl. Taste, then season with salt and pepper if desired. Cover with foil to keep warm. Wipe out the pan.

Pat the chicken dry with paper towels; season with salt and pepper on both sides. In the same pan, heat a drizzle of olive oil on medium-high until hot. Add the seasoned chicken. Cook 6 to 9 minutes per side, or until browned and cooked through. Leaving any browned bits (or fond) in the pan, transfer to a cutting board. When cool enough to handle, slice the cooked chicken crosswise.

The USDA recommends a minimum safe cooking temperature of 165°F for chicken. 

To the pan of reserved fond, add the sauce (carefully, as the liquid may splatter). Cook, stirring constantly and scraping up any fond, 2 to 3 minutes, or until slightly thickened. (For a thicker consistency, continue cooking the sauce. For a thinner consistency, add 1 tablespoon of water at a time to loosen.) Turn off the heat; stir in the butter until melted and combined. Taste, then season with salt and pepper if desired. Serve the sliced chicken with the mashed potatoes and cooked green beans. Top the chicken and potatoes with the finished sauce. Garnish the potatoes with the parmesan. Enjoy!