Mild and Sweet

1. Cut the carrots on a bias, or slight angle, into 1-inch pieces. Cover the carrots with about 1 inch of water in a saucepan. You don't need to peel young heirloom varieties, just scrub them well under cool-running water; peel mature carrots.

2. Season the water to taste with kosher salt and bring it to a simmer. Cook the carrots until tender, about 25 minutes, and drain them in a colander.

3. Warm 1 tablespoon each of butter and heavy whipping cream in separate saucepans over the lowest flame in the last few minutes of cooking the carrots. Offset the butter saucepan after it melts so it won't brown.

4. Return the carrots to the saucepan and add 1 tablespoon each butter and cream. Set the burner to warm.

5. Mash the carrots with the butter and cream to the desired texture using a potato masher or fork. Don't let the carrots sit in one place too long; keep them moving while they're on the heat.

6. Take the pan off the stove. Taste the carrots and adjust the seasoning with salt, heavy cream and butter to taste. Stir in lightly aromatic, freshly chopped herbs, such as parsley, lemon balm or lemon thyme.

Richly Caramelized

1. Heat the oven to 400 degrees Fahrenheit. Peel the carrots and slice them in half lengthwise.

2. Coat the carrots in olive oil and season them on both sides with kosher salt. Arrange the carrots cut-side down on a baking sheet lined with parchment paper or foil. Place the carrots in the oven.

3. Heat 2 tablespoons of butter for every pound of carrots in a saucepan over medium-low heat while you roast the carrots. Cook the butter until it turns brown and develops a nutty aroma, about 4 minutes; you'll see foaming on the surface and brown caramelized butter solids in the bottom of the pan.

4. Roast the carrots until caramelized and crackling, about 45 minutes. Transfer the carrots to a saucepan.

5. Add the brown butter -- and the caramelized butter solids -- to the carrots and set the heat to warm. Mash the carrots using a fork or potato masher until they reach the desired texture and taste them. Adjust the seasoning as needed with salt and pepper.

6. Take the pan off the stove. Add a squeeze of lemon juice to contrast the rich brown butter and sweetness of the carrots. Stir in fresh, aromatic herbs, such as rosemary and thyme, piquant spices, such as cumin and coriander, or the classic combination of fines herbes, namely chervil, chives, parsley and tarragon.