Place the vinegar, mustard, salt, pepper, egg, and lemon juice in a food blender, and mix for 30 seconds.
Slowly add the olive oil.
Blanch the carrots for 10 minutes in boiling water; then add the squash.
Cook for another 5 minutes, drain, and refrigerate.
When the vegetables are cold, toss them with a bit of the dressing, and serve as a vegetable side dish.