Prepare the cookie dough first, as this will need to rest in the fridge for approximately 60 minutes. In a large bowl, combine the flour, baking soda and salt. In another large bowl or the bowl of a stand mixer, combine the room temp butter, sugar, egg, and vanilla.
Use a hand mixer or the paddle attachment on the stand mixer to blend the butter, sugar, egg, and vanilla until combined. Slowly add the dry ingredients, mixing as you go, until the dough is well combined.
Remove the dough from the bowl, shape into a disc, cover with plastic wrap, and place in the fridge for approximately 60 minutes.
While the dough is cooling, make the carrot jam. Prepare the carrots by slicing them into large rounds until you have 3.5 cups worth. To get the other 0.5 cup of carrots, use a hand grater to shred 1 or 2 carrots. So, you will have 3.5 cups sliced carrots and 0.5 cup grated carrots.
Put the sliced carrots in a large pot and add just enough water to cover them. Bring to a boil and cook until soft, about 10 minutes. Drain the carrots and return them to the pot. Use a potato masher to roughly mash the carrots into a puree. Add the grated carrots, sugar, and lemon juice to the pot. Bring to a boil and then lower heat to medium. Cook for 12 to 15 minutes or until it begins to thicken. Remove from heat and store in a glass jar in the fridge to cool.
When the dough is ready, preheat the oven to 350 degrees F. Line two baking sheets with parchment paper. Take 1-2 tablespoons of dough at a time and roll it into a ball, then flatten it into a disk. Place on the baking sheets.
Use your thumb to make a thumbprint in the middle of each cookie. Add a scoop of carrot jam (the deeper your thumbprint, the more jam you can add). Bake for 15 to 18 minutes or until slightly browned.
Let cool for a few minutes before transferring to wire racks. Sprinkle with confectioner's sugar, and enjoy!