Preheat the oven to 325 degrees F.
Heat the oil in a frying pan, add the bacon and cook over medium heat for a few moments until fragrant. Add the morels, season with the salt and pepper and continue cooking until the mushrooms are lightly coloured and have given up any liquid that they contain (which won’t be much).
Add the leeks and thyme; continue cooking until the leeks are limp and tender.
Remove from heat and check the seasoning. Spread evenly on the pastry and sprinkle over the grated cheeses.
Beat the eggs and mix in the cream, milk and season with the salt and pepper.
Pour into the tart ring and bake on the middle shelf of the oven until just set (start checking at about 20 minutes). It should be slightly wobbly in the center.
Remove and serve warm or at room temperature.