Prehat oven to 450°F. Line a baking sheet with parchment.

In a small bowl, combine garlic, oregano, salt, rosemary, and black pepper. Use the back of a spoon to mash garlic into a paste. Add oil and stir to combine.

Place eggplant rounds on parchment and brush with oil mixture.

Roast in oven until very tender and slightly charred around the edges, about 40 minutes. Set aside.

Reduce oven temperature to 400°F.

Place lentils, shiitakes, and 1 1/2 cups of water in a medium saucepan over high heat and bring to a boil. Reduce heat to a simmer, cover, and cook until tender, about 30-40 minutes. Remove shiitakes, chop, and return to the pan. Remove from heat.

Heat oil in a large skillet over medium heat. Add onions, sprinkle with salt and pepper, and cook, stirring occasionally, until tender, about 7 minutes. Add garlic and cook an additional minute.

Add wine, tomatoes, cinnamon, cloves, bay leaf, paprika, and oregano. Reduce heat, partly cover, and simmer about 20 minutes. Remove and discard cinnamon stick, bay leaf, and cloves.

Add lentils and continue to simmer, uncovered, until all water has evaporated, about another 20 minutes. Stir in vinegar, taste, and add salt and pepper as needed. Set aside.

Melt butter in a large saucepan over medium heat. Add flour and stir until smooth, about 1 minute.

Add milk in three additions, whisking until smooth after each one. Add salt, nutmeg, ground cloves, and pepper to taste, and bring to a boil. Whisk in goat cheese until smooth and remove from heat to cool for 10 minutes. Whisk in egg yolk.

Lightly oil an 8x8 baking dish.

Place a layer of eggplant on the bottom, followed by the lentil mixture, spreading the surface smooth with the back of a spoon. Pour the bechamel over the top, smoothing into an even layer.

Bake 40 minutes, or until bubbling and bechamel is nicely browned.

Let stand 30 minutes before serving.