In a medium saucepan, cover sunchokes with 1 inch of cold water. Season generously with salt. Set over high heat and bring to a boil, then reduce heat to simmer. Let simmer for about 10 minutes or until tender.
Drain sunchokes and pat dry with a paper towel.
In a large cast-iron skillet, heat oil over medium heat until shimmering. Add sunchokes in a single layer and cook without moving until well browned about 3 minutes. Flip sunchokes, then add butter to the pan and allow to melt. Add a pinch of thyme to the melted butter and continue to cook, spooning butter over sunchokes, until browned on the second side, about 3 minutes longer.
Transfer sunchokes to a serving plate and spoon the thyme butter on top. Garnish with remaining freshly picked thyme leaves (if you have them)and sprinkle with flaky salt. Serve right away!
About the (awesome) tiny icons used in the menu bars: