Heat the remaining 1 tablespoon sun-dried tomato oil in a large nonstick skillet over medium heat. Add ¼ cup shallot; cook, stirring occasionally, until softened, about 4 minutes. Add sliced garlic; cook, stirring constantly, until fragrant, about 30 seconds. Add the reserved ⅓ cup cooking water; bring to a simmer. Gradually stir in cubed butter, one piece at a time, waiting until each is nearly melted before adding the next. Add thawed artichokes and rinsed beans; cook, stirring frequently, until heated through, 2 to 3 minutes.