Vegetable Maki with Quick Carrot-Daikon Pickles and Shiitakes

Make the pickles:
2 Peel the vegetables and slice them into thin matchsticks short enough to fit in a pint-sized canning jar. Pack them fairly tightly into the jar; you may not need them all. In a heat-proof measuring cup, stir the boiling water with the sugar and salt to until dissolved. Stir in the rice vinegar. Pour the brine over the vegetables in the jar; you may not need it all. Cover the jar and let the pickles sit for at least 30 minutes at room temperature or up to a few days in the refrigerator. To use, pull out a handful, dry on a paper towel, and roll!Cook the mushrooms:
3 Place the mushrooms in a colander and rinse briefly under running water (really, it's ok!). Shake dry. Trim off any brown ends and slice them 1/4-inch thick. In a wide skillet, heat the sesame oil until it shimmers. Add the mushrooms and salt and cook, stirring occasionally, until they're soft and golden, adding more oil to the pan if it looks dry. Deglaze with the mirin and taste for seasoning. Let the mushrooms cool a bit before rolling.