Melt 1 tablespoon butter in heavy medium saucepan over medium-high heat. Add tomato paste, garlic, and thyme; sauté 1 minute. Add wine and boil until reduced by half, about 8 minutes. Add both broths; boil until reduced to 1 1/4 cups, about 10 minutes. (Can be made 1 day ahead. Cover and refrigerate.)
Preheat oven to 450°F. Toast cardamom seeds in heavy small skillet over medium heat until fragrant, about 2 minutes. Cool. Transfer to spice grinder; grind coarsely. [I used a mortar and pestle.]
Sprinkle lamb with cardamom, salt and pepper.
Heat oil in heavy large skillet over high heat. Add 1 lamb rack; sear until brown, turning occasionally, about 6 minutes. Transfer lamb, meat side up, to baking sheet. Repeat with second lamb rack. [I was actually only using one lamb rack and so I seared it in my heavy oven-proof skillet, moved the lamb out, drained some of the oil — careful it's hot! — and then put the lamb back on the skillet instead of a separate baking sheet.
Roast until meat thermometer inserted into center registers 125°F for medium rare, about 18 minutes. Remove from oven and let stand 5 minutes. Cut lamb between bones into chops.
While chops are roasting: Bring sauce to simmer. Reduce heat to low. Add butter and mustard; whisk just until butter melts. Season with pepper.
Top with sweet mashed potatoes and lamb and serve. [I also lightly sautéed thin strips of bok choy, and wrapped them around the plated sauce. Seen in top photo.]