Preheat oven to 400 degrees F.
To pickle carrots, place sliced carrots in a large mason jar or two. In a medium saucepan, bring apple cider vinegar, water, sugar, salt and garlic clove to a boil. Pour over carrots to cover, let cool, and refrigerate for at least 2 hours. Pickles will keep for up to a week, and you should have some extra. Yay!
Place beets on a large piece of aluminum foil, drizzle with a little olive oil and sprinkle with a little salt. Wrap in the foil and roast for 1 hour or until tender. Rub off skin with a towel while hot (it's easier that way!) and let cool.
Put the almonds on a foil lined cookie sheet and roast for 5-7 minutes until toasted (they should smell toasty), careful not to burn!
Once beets are cool, slice thin (1/8 inch) and cut into rounds using a 1-inch cookie cutter. Try to get as many circles as you can from each slice.
Whisk together 1/4 cup olive oil, cumin, lemon juice, honey and salt to taste to make dressing and toss with sliced beets. Set aside.
Then make lemon cream. With a hand mixer or whisk, beat cream until peaks form. Then add in yogurt and lemon juice and beat until thick.
Spread some of the cream on the bottom of the serving plates, and then top with beets, carrots, almonds, mint, chili pepper flakes and a drizzle of honey. Serve immediately, as the beets will start to bleed a little if placed on the lemon cream.