In a large, nonreactive saucepan, bring 2 cups water, the vinegar, sugar, salt, coriander seeds, mustard seeds, peppercorns, cloves and bay leaf to a simmer over medium heat, stirring to dissolve the sugar. Cook for 5 minutes. Add the crushed red pepper and let steep for 5 minutes; strain.
Place the carrots in a large stainless steel or glass bowl. Add the hot pickling liquid, weighing the carrots down with a plate if necessary to submerge. Let sit until the mixture comes to room temperature. Serve the carrots with some of the liquid.