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1
Rinse the mustard seeds in a fine-mesh sieve, pat dry with paper towels, and place in an 8-ounce jar or heatproof bowl. In a heavy small saucepan, combine the rest of the ingredients. Bring the mixture to a boil over medium heat, stirring to dissolve the sugar. Pour the hot liquid over the mustard seeds and let them soak at room temperature until softened, 3 to 4 hours. Store pickled mustard seeds in a sealed jar or container in the refrigerator for up to 1 month.
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2
Prepare a charcoal grill for two-zone cooking and build a medium-high fire (or heat a gas grill to high). While the grill heats, place the carrots in a large mixing bowl, drizzle with enough olive oil to lightly coat, add the rosemary, and season generously with salt and freshly ground pepper and toss to combine.
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3
Grill the carrots over direct heat, until they have a nice char on both sides, using tongs to rotate around and the heat as needed for even cooking (and to prevent them from getting too dark), about 2 minutes per side. Move the carrots to indirect heat (If you're cooking on a gas grill, shut off one side of the grill), close grill, and cook an additional 2-3 minutes, until the carrots are just barely tender and then remove from heat.
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4
In the same bowl you used for the carrots, whisk together the pickled mustard seeds, vinegar, honey, 1/3 cup olive oil until combined. Place the arugula on a serving platter, top with the grilled carrots, drizzle with the pickled mustard seed dressing and garnish with flaky salt.
