Step 1
Toast panko in a 12-inch skillet over medium-high, stirring constantly, until golden, 4 to 5 minutes. Set aside.
Step 2
Cut carrots into thirds, and then cut each third in half lengthwise (or into fourths, depending on width of carrots).
Step 3
Heat oil in a cast-iron skillet over medium until hot. Cook carrots, flat side down, in hot oil, without turning, until tender, 10 to 12 minutes. (The cut sides will be very dark.)
Step 4
Remove skillet from heat; stir in ¼ cup water, honey, and sumac. Return to heat. Cook, stirring constantly, until most of the water has cooked off and carrots are coated, 4 to 5 minutes. Season with ½ teaspoon of the salt and ¼ teaspoon of the pepper, and transfer to an airtight container. Chill carrots about 30 minutes.
Step 5
Meanwhile, pulse feta and cream cheese in a food processor until blended, about 5 pulses. Add whipping cream, lemon juice, and remaining ½ teaspoon salt and ¼ teaspoon pepper. Process mixture until smooth, 2 to 3 minutes. Set aside until ready to use.
Step 6
Spread Feta Mousse onto bottom of serving plate, and top with carrots. Sprinkle carrots with toasted panko and mint before serving.