Place oven on low and rest a platter on an oven rack.
Add potatoes to a deep pot of boiling water; just enough to cover potatoes. Salt water and add potato halves. The potatoes will cook for about 12 minutes for fork tender.
Hold asparagus spears at each end. Snap asparagus tips from tough ends by bending spears. Place spears in a colander. Rest colander on top of the potato pot and place a cover over the colander. The asparagus will steam while the potatoes cook. Do this the last 5 or 6 minutes that the potatoes are cooking.
Potatoes will be just about done when the last of your trout is going into the skillet (method follows.) When the potatoes are tender, take a minute to drain them and return them to warm pot. Leave asparagus covered and set aside. Dress potatoes with chives, a drizzle of olive oil and a little salt. Leave in warm pot until trout is on the table, then transfer to a serving bowl.
Heat a large skillet over moderate heat. Combine egg and milk in a tin pie plate, beat with a fork. Place a cup of flour in a second pie tin and season well with salt and sparingly with pepper. Coat trout fillets in egg and milk, then in seasoned flour. Collect fillets on a plate until all of them are dredged and ready to be cooked.
Add 1/2 tablespoon extra-virgin olive oil to your skillet, half a turn of the pan in a slow stream. Add 1 1/2 tablespoons butter to the pan. When the butter foams, add trout and gently saute 4 fillets for 2 or 3 minutes on each side, until golden. Transfer trout fillets to warm platter in oven.
Return pan to the stove and add 1/2 tablespoon extra-virgin oil and 1 1/2 tablespoons butter. When butter foams, repeat cooking process. When all of the trout is cooked, add last tablespoon of butter to the pan. When the butter melts, add almonds and brown until lightly golden, 1 to 2 minutes.
Remove trout from oven and pour almonds over the platter. Garnish platter with chopped parsley, lemon wedges, steamed asparagus spears, and potatoes.