Peel the carrots and place them in a medium sized pan. Fill the pan with enough water to cover the carrots. Place this pan on a stove set to medium heat and let cover the carrots. Let the carrots cook for about 15 minutes. Uncover and test them with a fork to make sure they are softened (see recipe notes to cut down this prep time).
Drain and mash the carrots with a fork and set aside.
Peel and chop the onion and ginger.
Then, heat the olive oil in a skillet over medium heat. Add the chopped yellow onion and fresh ginger and temper or saute them for approximately 8 minutes, stirring occasionally, until the onion becomes soft and lightly golden.
Add the boiled and mashed carrots, sweetener, apple cider vinegar, smoked paprika, cinnamon, cardamom, and red chili powder into the hot pan, and stir well. Then, place the lid on the pan and let these ingredients cook for about 5 minutes.
Season with salt and black pepper to taste. Taste and adjust as needed.
This next step is optional and can be skipped if you prefer a chunky chutney. Transfer the mixture to a bowl and if the consistency isn't what you prefer, use an immersion blender to blend this until it is smooth. You can also add this to a small blender or food processor and blend until you reach your preferred consistency.