Melt the butter in a medium heavy-bottomed non-aluminum saucepan over low heat. Add the gooseberries and nasturtium flowers and cook until the gooseberries become soft and sauce-like. Put the mixture through a food mill fitted with its finest screen and set aside.
In another heavy bottomed non-aluminum saucepan, combine the fish stock and cream. Simmer over medium heat until reduced to a sauce consistency. Add the gooseberry/nasturtium purée and season to taste with salt. Keep warm over very low heat, or gently reheat for serving.
For garnish, put the handful of gooseberries and 1/4 cup of the fish stock in a small saucepan and simmer just until the berries are partly tender but still holding their shape, about 2 minutes. Set aside.
Season the trout fillets with salt and pepper. Heat a thin layer of olive oil over medium-high heat in a large skillet. Add the trout, skin-side down, and cook until the skin is nicely browned, 3 to 4 minutes. Turn and continue cooking until the fish is just opaque through the thickest part, 2 to 3 minutes longer.
To serve, arrange the trout fillets on individual plates and spoon the sauce over. Garnish with nasturtium flowers and the simmered whole gooseberries. Serve right away.