How to recreate this bought dish?

[Aparecium]

I bought these in Lidl recently, and they are very nice. But, as with so many of Lidl's lovelies, you never know when they're going to be in stock, or even if they'll ever return. So I'd like to recreate them at home.

You can see that they are quite soft when cooked, but the carrots are still slightly crunchy. (I added the piece of cheese on top, as the gratins are not intensely cheesy, and I had some cheese that was nothing special just sliced, but was very good melted.)

Any suggestions of a recipe/proportions of ingredients/techniques? The nearest thing to these that I have ever made would be quiche, and these are nothing like quiche.

Are they grated veg layered with cream and cheese like a potato gratin?

https://wholesomepatisserie.com/creamy-vegetable-casserole/

A recipe like this might work. It would taste similar.

In a small saucepan gently heat double cream (a pot) and either a small glass of wine, or a measure of vermouth, sherry or 125mls of chicken or veg stock. You could also add garlic, bay leaf, or any other seasoning you enjoy. Bring to the boil and leave to infuse.

Pre- heat oven probably around 160 fan but if you need it hotter for other stuff just check back on it sooner.

Finely slice your veg. Whatever you fancy. Potato and root veg are most commonly used but whatever you have in should work.

Butter whatever you intend to cook them in.

Either

Layer veg and cover with the cream mix making sure all the top of the veg is covered.

Or

Layer in about a third of the veg then add grated or crumbled cheese of your choice and repeat until full then cover with cream mix and top with cheese.

Loosely cover with foil or greaseproof Paper and bake for around 30 minutes, remove cover and continue baking for another 20-30 minutes. Obviously you’ll need shorter baking times if you do little individual ones.

But generally it’s a fairly adaptable dish.