Preheat the oven to 325°F.

Place the olive oil in a large skillet over medium high heat.

Add the ground beef and cook for about 3 minutes until lightly browned. Stir frequently.

Add the onions and cook for 5 minutes. Stir frequently.

Add the mushrooms and cook for 7 to 10 minutes. Stir frequently.

As the mushrooms cook they will begin to give up some water and steam. As the water begins to evaporate from the mushrooms they are cooked enough.

Add the tarragon, Worcestershire sauce, mustard, honey, vinegar, and salt.

Cook for about one minute and add the flour, stirring thoroughly to incorporate.

Cook for about one minute and add the vegetable stock.

Add the milk and cook for about 2 minutes, stirring frequently, until the sauce begins to thicken. Remove from the heat.

Place a layer of lasagna noodles in the bottom of the Pyrex dish.

Spread 1/3 of the mushroom mixture over the top of the noodles.

Add a layer of noodles and 1/3 of the mushroom mixture.

Add half of the cheese to the second layer.

Add a third layer of the lasagna noodles and top with the remaining mushroom mixture.

Cover the Pyrex dish with foil and bake for 45 minutes.

Remove the foil from the top of the lasagna and place a layer of the sliced cheese across the top of the lasagna.

Bake for about 5 minutes and serve.