Step 1

Stock: Simmer stock, mushrooms, lemongrass, ginger, cinnamon, garlic, cardamom, cloves, and fenugreek leaves, if using, in a large saucepan, uncovered and stirring occasionally, over medium heat until slightly reduced and very fragrant, 30–40 minutes. Strain through a fine-mesh sieve into a large bowl or measuring cup; discard solids.

Step 2

Do Ahead: Stock can be made 3 days ahead; cover and chill.

Step 3

Curry: While stock is simmering, melt butter in a small skillet over medium-high heat. Cook flour, stirring constantly, until roux is golden brown and smells nutty, 2–4 minutes; set aside.

Step 4

Heat oil in a large wide saucepan (you want a wide pot for maximum evaporation) over high. Cook mushrooms, undisturbed, until browned underneath, about 2 minutes. Toss and continue to cook, undisturbed, until browned on second side, about 2 minutes. Continue to cook, tossing occasionally, until browned on all sides and tender, about 2 minutes more; season with salt and pepper. Using a slotted spoon, transfer mushrooms to a medium bowl, leaving oil in pot.

Step 5

Reduce heat to medium. Cook onion, carrots, and celery, tossing occasionally, until tender, 8–10 minutes. Pour in sake and cook, scraping up brown bits on bottom of pan, until liquid is evaporated, 2–3 minutes. Sprinkle curry powder and garam masala over and cook, stirring frequently, until very fragrant, about 1 minute. Add potato, apple, mushrooms, and reserved stock and bring to a boil. Whisk in reserved roux until mixture thickens. Reduce heat, bring to a simmer, and continue to cook, uncovered and stirring occasionally, until mixture is very thick, almost the consistency of yogurt, 25–30 minutes. Stir in brown sugar and vinegar; season with salt.

Step 6

Katsu and Assembly: Pound pork chops between 2 layers of plastic wrap to ¼" thick. Place flour in a shallow bowl (a pie plate works best). Place eggs in another shallow bowl. Place panko in a third shallow bowl. Season flour, eggs, and panko with salt and pepper.

Step 7

Working one at a time, season cutlets with salt and pepper, then dredge in flour, shaking off excess. Transfer to bowl with egg and turn to coat. Lift from bowl, letting excess drip off. Coat in panko, pressing to adhere, then transfer to a rimmed baking sheet.

Step 8

Heat 3 Tbsp. oil in a large skillet over medium-high. Cook 2 cutlets until coating is deep golden brown and pork is just cooked through, about 4 minutes per side. Transfer to a plate. Wipe out skillet and repeat with remaining 3 Tbsp. oil and 2 cutlets.

Step 9

Slice pork into 1" strips. Arrange rice and curry side by side on a plate or in a shallow bowl. Top with pork, scallions, and fukujinzuke.