Set your oven to 400°F
Chop up all of your vegetables and put them into a bowl. In the meantime, melt your butter and oil together in a pot.
Once the butter has melted, add your vegetables to the put, stir to make sure that they have all been covered with the butter. As soon as they have, cover the pot with a lid.
Check every few minutes to stir but you are going to sweat your veggies for about 10-15 minutes. You want to make sure that they are really soft.
You will then add your flour, make sure to coat all of your vegetables.
Add half of your milk, and stir your vegetables. It will begin to thicken. Once thick, add the rest of your milk.
Once you have stirred your mixture and it appears to be thickening, add your vegetable bouillon. You also now want to add the thyme, and any salt or pepper you wish to add.
Allow this mixture to sit on medium for about 10 minutes.
Transfer to the dish in which you will cook it in, and cover with tater tots.
Place your vegetable tater tot casserole in the oven and bake for 30 minutes.
When done, remove from oven and allow to stand for 5-10 minutes prior to serving.