Set oven to 425°F. Dampen carrots. Place salt in hotel pan and roll carrots in salt until well coated. Roast until softened, about 40 minutes.
In a bowl combine oil, caper brine, rice vinegar, brown sugar, smoked paprika, and dill. Whisk to dissolve sugar and set aside.
Once carrots have softened, remove from oven and cool. Rinse off excess salt. Use a peeler to cut thin slices of carrot. Toss with caper brine mixture and store in an airtight container refrigerated for 1-2 days. Use as desired.
Roasting time will vary based off the size of carrots, roast until they are cooked through completely but not mush after cooling.