Toss the Jerusalem artichokes, garlic, onion and butter on half sheet tray; cover with aluminum foil. Roast at 350°F for 1½ hours or until fork tender (the consistency will not be as tender as potatoes due to their fibrous texture).
Transfer artichoke mixture to food processor. Add sour cream, salt and pepper and purée until smooth; fold in cut chives. Makes about 2½ cups.
For the bone-in pork chops:
Sprinkle pork chop with ¼ teaspoon each salt, pepper and garlic; rub both sides with 1 tablespoon fresh herbs. Heat a large sauté pan over medium-high heat. Add 2 tablespoons butter, melt slightly, then add the pork chop and 2 thyme sprigs; cook for 2 minutes on each side, spooning butter from pan over pork chop to baste. Transfer pan to oven and roast at 350°F for 10 minutes or until the internal temperature reaches 145°F.
For the brown butter mushrooms & peas:
Add 1½ tablespoons butter to large sauté pan over medium heat; whisk until butter begins to brown. Add ½ cup mushrooms and cook for 3 minutes, stirring. Add 1 teaspoon shallots and ½ teaspoon garlic and cook for 1 minute, stirring. Stir in ⅓ cup peas, ¼ teaspoon salt, ⅛ teaspoon pepper and ½ teaspoon lemon juice. Cook for 2 minutes or until peas are heated through,
Place Jerusalem artichoke mash and brown butter mushrooms & peas on serving plate. Remove pork chop from pan and lean onto mash.
Add ¼ cup chicken broth to pork chop pan and cook over high heat until reduced by half; whisk in 1 tablespoon butter. Spoon pan broth over pork chop.