Put a large skillet with a lid over medium heat and let it warm for about 1 minute.

Add the olive oil to the skillet and swirl to coat the bottom.

Add the sliced mushrooms to the skillet in an even layer.

Cook the mushrooms without stirring for 4 minutes so they can brown on the first side.

Stir the mushrooms and cook for 3 to 4 minutes more, until they have lost their moisture and look well browned at the edges.

Add the sliced shallot to the skillet with the mushrooms.

Cook the shallot for 2 minutes, stirring often, until it softens.

Add the sliced garlic to the skillet and cook for 30 seconds, just until fragrant.

Put the drained lentils into the skillet. Add the Dijon and 1/3 cup water.

Stir everything together and season with salt and black pepper. Cook for 2 to 3 minutes, until the lentils are hot and the liquid has lightly coated them instead of pooling in the pan.

Use the back of a spoon to make 4 shallow wells in the lentil mixture.

Crack 1 egg into each well, placing the eggs directly into the skillet.