Prepare the vegetables: slice the onions julienne, shred the carrots and the celeriac (a food processor works perfect for this step), slice thinly the peppers and the green tomatoes.
In a large pot, bring to a boil the water, vinegar, sugar, salt, pepper and bay leaves.
When the sugar dissolves and the mixture comes to a boil, throw the vegetables in the pot in the following order: carrots, celeriac, onions, peppers and finally the green tomatoes.
Bring the pot back to a boil and keep the vegetables only 3 minutes from the time the pot started to boil again.
Remove them with a spatula and place them in a large bowl.
You will NOT need the vinegar and water solution anymore after that.
Whisk the mustard and the oil separately, like a mayonnaise.
Pour the mustard sauce over the mix of vegetables in the bowl and mix well.
Fill up the jars with this hot vegetable mixture, close the jars tight and process the jars for 10 minutes in a boiling-water canner.
Keep the jars in a cool, dark place and consume them in the next 6 months.
Serve this vegetable mixture as an appetizer, salad or next to roasted meats in the winter.