Culinary definition of mirepoix: Finely diced or minced sautéed vegetables used in traditional French cooking.
C@H FOOD FOR THOUGHT
Not just French cooking - pretty much all cooking. But how much of each, and when? Typically, the mixture comprises 50% onion plus 25% each celery and carrot. But that's tradition, not the rule: maybe go light on the acid (onion) and heavy on the sweet (carrot/celery) or visa-versa, when the recipe or (more important) your instincts dictate.
Onion often goes in first, in a small amount of oil (we use top-quality olive oil like Domenic Fiore over low temperatures, and recommend adding butter for its beautiful, natural sweetness) and should be rendered 'very slowly' with much stirring, to soften without colouring. Sweet potato and turnip can pinch hit for carrot ... well, in a pinch. Final note - in Louisiana, the defacto triple mix is known as 'The Holy Trinity' and comprises onion, celery and bell pepper. So, if you are cooking anything remotely Cajun or Creole, adjust accordingly.
✭ ✭ ✭ Purists will argue the point, but us time-starved everyday gourmets advocate saving diced carrot, celery and onion in separate re-usable containers in the kitchen freezer, marked with quick dissolve labels. It's the 'prep' after all that most often keeps us from cooking well and often. Just be sure to keep the onion in a tightly sealed container so your ice and ice cream don't get stinky. Note however that thawed veg tends to hold and release more water than fresh, which will extend the time it takes to colour properly in the pan - don't be tempted to turn up the heat to compensate. Be patient. Thaw vegetables in the refrigerator overnight if at all possible, as they will maintain their firmness, integrity and water much more effectively than if defrosted at room temperature.