How to Make It
In a large saucepan, combine the water, vinegar, sugar, thyme sprigs, garlic, peppercorns, crushed red pepper, mustard seeds and salt and bring to a boil. Simmer over low heat for 10 minutes. Remove from the heat and let cool for 5 minutes. In a wide heatproof bowl, cover the carrot slices with the pickling mixture. Let cool to room temperature.
In a large saucepan of boiling salted water, cook the asparagus until bright green, about 1 minute. Drain and refresh under cold water. Add the asparagus to the pickling mixture and refrigerate for 24 hours. Drain the pickles, transfer to a platter and serve.