Peel and finely dice the garlic and 1 shallot; place in a small bowl. Cut the basil into thin strips and add. Pluck the thyme leaves from the stems and add. Finely chop the parsley and add half of it to the herb mixture. Mix with the olive oil, season with salt and pepper. Rub and fill the trout inside and out with this herb mixture. Refrigerate for 1 hour if time permits.
Melt the butter in a large pan over medium-high heat. Coat the trout in flour and brown on all sides for about 3–4 minutes until golden. Reduce heat to medium-low and continue cooking for 8–10 minutes, turning occasionally, until the thickest part reaches 63 °C (145 °F). Transfer the trout to a warm plate.
Pour the white wine into the pan to deglaze, scraping up any browned bits. Add the remaining shallot (peeled and diced) and the remaining parsley. Simmer for 2–3 minutes until slightly reduced. Stir in the whipped cream and simmer for 1–2 minutes more. Season with salt and pepper to taste.
Arrange the trout on plates and pour the sauce over. Serve immediately, optionally with parsley potatoes and a green salad.