Melt the butter in a wide saucepan. As soon as it foams, add the lemon juice and sugars. Stir over low heat until sugar is melted.
Add the carrots, stir so that all the carrots are coated in the caramel sauce. Season with salt and pepper, half cover the pan and simmer for 25 minutes, stirring regularly.
The carrots are done when they are shiny and still a little firm in the centre.
Sprinkle with chopped parsley and serve immediately.