Pour 1 tablespoon olive oil into a large frying pan over medium-high heat. When hot, add carrots, sprinkle lightly with salt, and turn to brown on all sides, about 4 minutes total. Remove from pan.
Add onion, celery, and garlic to pan; stir often until vegetables are soft but not browned, about 2 minutes. Add tomatoes, chicken broth, orange, thyme, and the carrots to pan. Bring to a simmer, cover, and cook, stirring occasionally, until carrots are very tender when pierced, about 1 hour.
Meanwhile, pour remaining tablespoon olive oil into a small frying pan over medium-high heat. When hot, add capers and cook until they begin to peel back, about 1 1/2 minutes.
Spoon braised carrots into a serving bowl or onto plates and top with capers and parsley.
Wine pairing: Aromatic but crisp Viognier, with honeyed citrus and a few minerals. Best in our pairing: Miner Family Simpson Vineyard 2004 (California; $20), Eberle Mill Road 2004 (Paso Robles, CA; $18), and R.H. Phillips EXP 2003 (Dunnigan Hills, CA; $14).
Flavor bridges: The classic honey-tangerine notes in a totally dry Viognier seem sweet and throw a line to the sweetness in carrots. The orange in this dish clinches the deal. Aromatic, floral qualities in the wine give it weight; long braising does the same for the carrots. Minerals under the wine's fruitiness link to the briny capers.
Note: Nutritional analysis is per serving.