Place an oven rack on the center shelf and preheat the oven to 350°F. Grease a 2-quart baking dish.
Heat the olive oil in a large saucepan over medium heat. Add the carrots and onions. Stir for a couple minutes, then cover, reduce the heat to low, and cook for 15-20 minutes, or until carrots are fork-tender.
Transfer the carrots and onions to a food processor. Add half of the milk, then pureé until smooth.
Transfer the pureé to a large bowl and add the remaining milk, cheese, butter, flour, salt and pepper, stirring to combine.
In a separate bowl, whisk the eggs together for about 30 seconds. Stir the eggs into the carrot mixture until evenly combined.
Transfer the mixture into the prepared baking dish and bake for 45-50 minutes, or until the souffle is puffed up slightly and lightly golden. Let cool for 5 minutes before serving.