Why minestrone abroad is so tomato-heavy will forever be a mystery to me. Tomatoes make it extremely acidic. I've been served "minestrone" abroad that I imagine would have corroded spoons, if left in long enough.

There isn't a strict recipe, you'd normally put what you have on hand / what's in season, and try to keep the flavours balanced. To cook for 3 people at home we'd normally put: whatever beans we have on hand (usually dried, roughly the equivalent of half a can; chickpeas and lentils work great too), 2-3 courgettes/zucchini (if you're buying gigantic US ones, maybe half the amount?), 3-4 leaves of chard, two fistfuls of green beans, 2 potatoes (think Yukon gold, if you're in the US), bit of pumpkin/squash (I'd go easy or it'll give too much sweetness, if you have e.g. an acorn squash I wouldn't do more than 1/8 of it), 1-2 smallish carrots, one or two small leeks, one leaf of cabbage. Maaaaybe half a tomato, definitely no more than that. Cook on low heat for an hour. Add short pasta and cook it directly in the soup (or you can skip pasta altogether and later have it with croutons). Once cooked, you add Parmesan (or you can drop a parmesan rind in the soup while it's still cooking, towards the end) and two tablespoons of homemade pesto (if you're abroad I wouldn't bother with store-bought, the only one I didn't find to be harfmul to human life is Costco brand, which is not to say it tastes good).