Preheat oven to 400°F Trim ends off green beans. Cut into 1" pieces. Core pear and cut into ½" slices. Peel and halve shallot. Cut into ¼" slices. Mince garlic. Stem and mince thyme. Pat pork tenderloin dry, and season all over with ¼ teaspoons salt and a pinch of pepper.
Heat 2 teaspoons olive oil in a large non-stick pan over medium-high heat. Add green beans, pear, shallot, ¼ teaspoons salt, and ¼ teaspoons pepper to hot pan. Stir occasionally until lightly charred, 5-7 minutes. Transfer to prepared baking sheet and spread into a single layer (some overlap is ok). Reserve pan; no need to wipe clean.
Return pan used to start green beans and pear to medium-high heat. Add 1 teaspoons olive oil and pork tenderloin to hot pan. Cook until browned on two sides, 3-4 minutes per side.
Place pork tenderloin on top of green beans and pear. Roast in hot oven until pork reaches a minimum internal temperature of 145 degrees, 16-18 minutes. Rest pork at least 5 minutes, then slice if desired. Reserve pan; no need to wipe clean. While pork rests, make sauce.
Return pan used to sear pork tenderloin to medium heat. Add 1 teaspoons olive oil, garlic, and thyme to hot pan. Cook until fragrant, 30-60 seconds. Stir in ¼ cup water and chicken base. Cook until slightly thickened, 1-2 minutes. Remove from burner and swirl in butter. Season with ¼ teaspoons salt and a pinch of pepper.