Place the yeast and milk in a small bowl or cup and stir to dissolve yeast. Leave for 5 minutes or until foamy. Add the flour, eggs, yeast mixture and sea salt to the bowl of a stand mixer fitted with a paddle attachment and mix until the dough comes together. Switch the paddle attachment for a dough hook and knead, gradually adding the olive oil, a tsp at a time, allowing the oil to become fully incorporated before adding more. For a little bit it will look like a hot oily mess, but stick with it, the oil will mix into the dough with a little patience. Knead for 10 minutes or until the dough smooth and elastic. Cover dough with a tea towel and leave in a warm place for 1½ to 2 hours or until doubled in size.
Knock back the dough and place on a tray covered with baking paper that has been lightly floured. Press down and use your fingers to shape into a rough circle. Lightly brush the top with more oil and cover with a tea towel and leave an hour or until doubled in size. While the dough is rising preheat the oven to 220 celsius (425 Fahrenheit) and cook the toppings.
Place a frying pan over a medium-low heat. Split the leek in two lengthways and slice roughly 1.5cm (1.2 inch) thick. Add half the olive oil to the pan and gently fry the leeks until soft. Add the garlic, salt and white wine and bring the pan to a simmer before reducing the heat to low. Simmer until almost all of the wine has been absorbed. Remove from the heat and add the Dijon Mustard and stir well to combine.
Place another frying pan over a medium high heat. Add the remaining oil and the mushrooms and cook until lightly golden. Season with salt and pepper and add the thyme leaves. Stir well to combine and remove from the heat.
Once the toppings have cooled top the tart with the leeks, leaving a border at the edge of the tart. Top the leeks with the mushrooms and brush the edges of the tart with the egg wash. Bake for 15 to 20 minutes until the tart crust is golden and the underside of the tart is cooked.
While the tart is baking make the cashew cream drain the cashews and place in a blender along with the water and mustard. Blend until smooth and season to taste.
When you are ready to serve drizzle the mustard cream over the tart and serve.