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I do these things off the top of my head, so bear with me. The following serves two or three as a side dish.
Run a small can of drained pineapple, a teaspoon of fresh ginger root (one thick slice), a teaspoon of peanut oil and one third of the retained pineapple juice through a food processor. More or less ginger to your taste. Heat in an oiled wok, a film of oil not a pool. Watch it as the pineapple sauce gets very hot before it boils. If it does begin to boil, turn down the heat. You want a mild simmer at the most.
I prefer cooking julienned carrots but thinly sliced work as well. A mix of both has a nice look. Cook as many carrots as can be coated with the pineapple sauce until they are just tender. Keep on eye on it and stir often as all the sugar in this can scorch easily. Add as little pineapple juice as needed. If it needs thickening (usually it won't), add a bit of cornstarch to the remaining pineapple juice. Add this to the wok, it should thicken fairly quickly.
Other possible ingredients: salt or soy sauce, butter, garlic, nutmeg, sugar (yeah, you can make it sweeter still), hot pepper sauce (if the ginger isn't enough heat already). I don't recommend trying cayenne pepper until you've cooked it a few times and have a good feel for how ginger cooks. OTOH, pepper sauce or cayenne turns the sauce a bit more orange to match the carrots.
This may sound easy, and it should be for an experienced cook, but watch it because if it starts to boil, it is also very close to burning. Even if it doesn't burn, it could easily ruin a non-stick wok; a properly seasoned wok though will do just fine. You can not turn your back to this dish as it cooks. The thinner the carrots, the quicker they cook, and the more likely this dish will succeed. I have cooked this well over a dozen times and I still get the occasional disaster.
If all goes well, your carrots should be very nicely glazed and will retain their flavor. The basic dish is somewhat spicy and very sweet. Mint leaves and a little paprika make a nice presentation.
Our garden:
Not many of the tomatoes survived planting, I think it was that freak frost. The green beans and squash are doing fine. The carrots have even taken root in one of the big external bins we use. However fire ants have discovered that bin, which makes things tricky. The blackberries didn't take and I'm still in mourning over that.