Cut off the stalks from the fennel bulbs and cut each bulb lengthwise into 6 thick slices.
It’s important that you do not remove the core otherwise the slices will fall apart.
Season each fennel slice with a little bit of salt and pepper.
In a large heavy skillet, heat a little bit of olive oil or coconut oil over medium-high heat until your pan gets really hot. Add the fennel slices and cook until nice and brown, then flip the slices and cook the other side.
Lower the heat, cover and continue cooking for about 6-8 minutes, until the fennel is good and tender.
For the fish fillets
Pat the fish dry and season with a little bit of salt and pepper.
Heat a little bit of olive or coconut oil in a medium non-stick skillet, over medium-high heat. When pan is hot enough, add fillets and cook until it starts to form a little bit of a brown crust and flesh turns almost completely opaque. Very delicately flip the fillets and continue cooking until fish is cooked all the way through and no longer translucent. This should take about 1½ to 2 minutes per side, depending on thickness.
Sprinkle with lemon or lime juice and transfer to dinner plates
Serve with braised fennel, loaded coleslaw and fresh greens.