Cover rice with plenty of water in a medium pot and add a pinch of salt. Put over high heat and bring to a boil. Reduce to medium and cook at a strong simmer for 40 minutes - 1 hour, or until rice is tender with a pleasant chew or bite. Drain rice and stir in 1 teaspoon butter until melted.
Season the fish cheeks on both sides with salt and pepper. Set aside.
Heat the lard or oil in a skillet over medium-high heat. Add the morels and cook until well-browned and crispy. Remove from pan and set aside, leaving the oil behind. Increase heat to medium-high and add the fish cheeks. Sear hard until golden, then flip, add the other teaspoon of butter and sear until just cooked through. Remove from pan and set aside.
Reduce heat to low and add the vermouth and morels back to the pan. Cook for 2 minutes. Add the cream and half the parsley/chives and cook until the liquid turns into a clinging sauce. Remove from heat.
Split the rice between two plates, then arrange half of the cheeks on each plate. Drizzle the sauce over the cheeks, and scatter the plate with the remainder of the parsley or chives.