Cut florets from broccoli, then chop up the stems into matchstick-ish pieces. This chopping of the stems is the only way I can get my children to eat the stem part of the broccoli. They feel it is inferior, and will not ever consume it unless it looks nothing like broccoli stems. Last night, they were convinced it was celery, and would not hear otherwise. I win!
Peel carrots, cut into pieces that are about the same size as your broccoli stems. This way, they will be done at the same time as the broccoli stems.
Heat a large skillet, and pour in a happy amount of olive oil. The idea here is not to boil or poach your veggies in oil, that would be gross and you wouldn’t taste the veggies’ loveliness, only the oil. And that is not the point of sautee-ing your green guys.
When the oil is shimmery, it is hot enough for a saute. If you are a particular sort of cook, put the carrots and broccoli in the pan for a few minutes before you add the asparagus. If you are me, dump everything into the pan at once.
If you are that particular cook, get out your measuring spoons and put 1 1/2 teaspoons of thyme in the pan. If you are me, you would grab a big pinch of thyme. And then another, and then possibly another. I love thyme. Cook over medium- to medium-high heat until the veggies are the brightest-colored version of themselves.
Eat a carrot. If it is too crunchy, pour 1/2 cup of water into your pan, cover and let the veggies steam for a minute or two. And voila, you are done.
If you are feeling super saucy, put a little vinegar on them before you eat.