In a small bowl, combine the lemon juice and the saffron. This process is called "blooming" and allows the saffron to open up in flavor and color. Set aside.
Heat a skillet large enough to hold all four fillets. Medium heat.
In a bowl, combine the flour, coriander, and red pepper.
Dredge the fish fillets in the flour and fully dust off, as if to try to remove almost all of the flour. Transfer back and forth between your hands, gently patting. If you've ever seen a tortilla made by hand, use that same motion.
Add the olive oil and butter to the pan. Swirl and warm the butter until its aroma is toasty and starts to foam.
Gently slide the fillets into the pan, skin sides down, leaving a fair amount of space between them.
Now, don't move the fillets until the edges start to brown a bit, like a properly made pancake. This should take about 4 minutes. It's better to adjust the flame than to rustle with the fish. I promise.
Using a thin fish turner, flip the fillets. Season with salt. Cook for another 2 minutes or so, or until one sacrificial piece (yours) flakes off nicely, but is still translucent. Transfer the fillets to a plate for a moment while you cook the vegetables.
Add the fennel, onion, and garlic to the pan. Cook 1 minute. Turn the heat to low and continue to stir and sweat the vegetables until translucent, about 2 more minutes.
Now, add the tomato and saffron mixture. Raise the heat to medium, stir, and sauté until saucy. Sprinkle with the parsley.