I don't inject insulin, but I am following a very low carb diet. My favourite carbs are veggies! Avocado is definitely one of my favourites!
Artichokes - cooked from fresh, dipped into mayo vinaigrette - yum and super healthy for the liver too.
Asparagus - I have it a couple of times per week, usually chopped and sauteed with bacon bits, then break a couple of eggs on top. Also love the spears grilled with olive oil, or wrapped in prosciutto and baked.
Cavolo Nero, or any type of kale - sauteed in butter so some bits get crispy, with coarse sea salt on top.
Kohlrabi - only raw, like beetroot (very rarely) and Mooli radishes; they all have some sweetness but don't spike me
Mushrooms of every type, in every incarnation (sauteed in bacon grease, grilled with butter, in soup, added to meat, sauces...)
Peppers, courgettes, aubergines - love them grilled or roasted with lots of garlic (peppers raw as well)
OK, I could continue listing loads of vegetables I enjoy, but the gist seems to be - as long as they are eaten with fat (butter, vinaigrette, oil, cream) or contain fat (like avocado), the impact of the carbs on BG is slowed down.