While I use sturgeon here, there is no reason you cannot use any firm fish. Codfish springs to mind, as would tilefish, snapper, drum, a large pike or walleye, trout or salmon. Use whatever. Go for it.
Salt the fish well and set out on the counter while you prep the other vegetables.
Put the carrots in a food processor and buzz until the pieces are all very small, but it's not a puree. Put the carrots in a small pot with 1 quart of water and bring to a simmer. Simmer gently for 20 minutes and strain through a fine-meshed sieve with a piece of paper towel set inside. Either clean the pot and pour the broth back in or pour it into a new pot. Salt the broth to taste and keep warm.
Preheat the broiler on high. Coat the asparagus with 1 tablespoon of the olive oil and salt well. Put the asparagus in a shallow pan or baking sheet and roast under the broiler until slightly blackened, about 6 minutes. Remove and cut into pieces you can eat in a bite or two. Set back in the turned-off oven to keep warm.
Put 2 tablespoons of olive oil in a saute pan and get it very hot. Pat the fish dry with paper towels and lay the pieces down on the flatter side of the fillet. Let this cook over medium-high heat undisturbed for 2 minutes. Use a spoon to baste the top of the fish pieces with the hot oil; you'll need to tilt the pan to do this. You want to baste the fish until it turns opaque, about 15 seconds or so. Keep searing the fish until you can see the edge begin to brown. Gently use a spatula to try to move the fish. It should come away cleanly, or stick in maybe one spot. If it's still glued to the pan, keep cooking it. When the fish comes cleanly off the pan, move it to a plate and set it in the oven to stay warm.
Add the last tablespoon of olive oil to the saute pan and add the spinach. Saute the spinach until it wilts, and add the peas. Cover the pot and lower the heat all the way. Let the vegetables steam for a minute or two. Uncover the pan, add salt and black pepper.
To serve, put down some of the peas and spinach on everyone's plate and top with a piece of fish. Give everyone some asparagus, pour in some carrot broth and top with the caviar if you are using it. Serve with crusty bread.