Classic Moussaka with Eggplant, Spiced Lamb Ragu

3 eggplant, about 1 to 1¼ lb each, cut into 1/3-inch rounds

2 tsp kosher salt

1 cup olive oil, divided

1 ½ lb ground lamb

1 yellow onion, finely chopped

4 clove garlic, minced

1 can crushed tomatoes, 14 oz, no-salt-added

2 tbsp tomato paste

1 cup dry red wine

1 cup beef broth, low-sodium

1 tsp ground cinnamon

½ tsp ground allspice

¼ tsp ground nutmeg

1 bay leaf

1 tsp granulated sugar

¼ cup fresh parsley, chopped

6 tbsp unsalted butter, divided

⅓ cup all-purpose flour

3 cup whole milk, warmed

2 egg yolks, room temperature

1 cup grated Parmesan, freshly grated, divided

1 tsp freshly ground black pepper

¼ cup dry breadcrumbs

1 tbsp butter (for baking dish), for greasing