Make the dough by weighing the fat of your choice and the plant milk in a microwave proof jug and heat up until warm.
In a large bowl add the flour, salt, sugar and yeast. Gently pour the milk & fat mixture and the water, and start mixing with a fork or spatula.
Keep mixing for a good 5-10 minutes and don't be worried if dough will result too wet, that's exactly how is it meant to be like!
Cover with some film and allow to double up its volume (between 1 up 2 hours, depending on the surrounding temperature).
Clean the vegetables according to recipe notes, then roughly chop the mushrooms and sauté for a few minutes in a pan with a clove of garlic, some olive oil and thyme. Season with salt and pepper to taste and set aside.
In another pan (or use the same one you sautéed the mushrooms in after giving it a rough clean with a kitchen paper), melt some vegan butter, add leek slices and cook undisturbed for 6-7 minutes. Flip the slices over, season with salt & pepper and cook for another 6-7 minutes.
Allow both types of vegetables to cool down to room temperature before moving onto the next step.
As soon as the dough has doubled its size, transfer it into a 20x30 cm well-oiled* baking tray with deep sides (*if you don't want to use too much oil you can line the tray with some baking paper lightly greased).
Spread it all over and allow it to sit for another 30 minutes/1 hour.
Sprinkle some olive oil on top and dimple the dough by firmly press down with the tips of your fingers.
Arrange the cooked mushrooms and leek slices on top of the dough, gently pressing them down. Season with salt flakes, freshly ground pepper and thyme sprigs.
Preheat the oven at 200° C (390°F) and bake the Fluffy Brioche Focaccia with Leeks and Mushrooms for 30 minutes or until top turns golden.
Enjoy the Vegan Brioche Focaccia warm or at room temperature.