Quite a quandary..
If they put your blood glucose up, things like mashed potato are going to have to go out the window. You could experiment first, and find out whether mashing them with cream and butter not milk, makes a difference. You could also try smallish baked jacket spuds or sweet potatoes, eating with plenty of butter or scooping out the spud and mashing it with butter or butter and cream.
A researcher found that if you boil new potatoes, drain and rinse under cold water then leave in the fridge overnight, when you re-heat the next day, they don't spike people quite as much.
You can mash cauliflower really simply. Just boil as many cauliflower florets as you want, drain, and add cream and cream cheese, and mix until smooth, adding salt and pepper.
With peas, it's about portion size, 2 tablespoons of frozen peas (80g) is around 6g carbs. 2 tablespoons (80g) of drained tinned sweetcorn is around 9g carbs.
I would suggest using oven, slow cooker, pressure cooker or microwave and just bunging things in, rather than a lot of messing about with saucepans - or buying a tiered electric steamer - it would be really good with salmon, for example. You can buy soupmakers too. Another suggestion is to use a deep fat fryer to make chips out of swede, carrots, even zucchini, rather than spuds.
You don't have to change anything about the meat, fish and chicken recipes apart from cut down gravy or cut it out if it spikes your blood glucose.
I suggest looking for recipe books which aim for meals in minutes or one pot cooking. You could borrow some from the library maybe and come back to the forum to check whether the ingredients are likely to spike you.
Some root veg might be okay, others not. You might do better with fennel, radishes and swede than you do parsnips, beetroot and spuds. Testing your BG after eating them will show you.
There are still plenty of vegetables that you can eat e.g. runner beans, spinach, kale, spring greens, asparagus, samphire, green beans, Brussels sprouts, cabbage (red, white, Savoy, Sweetheart), kohl rabi, gem squash, aubergine, pumpkin, tomatoes, cucumber, celery, radishes, leeks, onions, globe artichokes, to name a few.
As for the other half, if you do the cooking, you're the boss !