Finely chop the leaves of the Flat-leaf parsley and mince the Garlic; set both aside so they’re ready to finish the sauce.
Warm a heavy saucepan over medium heat and add the Extra-virgin olive oil; when it shimmers, add the minced garlic and sauté briefly until fragrant but not browned, about 30–45 seconds.
Sprinkle in the All-purpose flour and whisk continuously to form a pale blond roux, cooking for about 1–2 minutes to remove the raw flour taste.
Pour in the Dry white wine, scraping the bottom of the pan to deglaze, and let it simmer until the alcohol cooks off and the liquid reduces slightly, about 2–3 minutes.
Slowly whisk in the Fish stock and bring the mixture to a gentle simmer; cook until the sauce thickens to a spoon-coating consistency, about 4–6 minutes.
Remove the pan from the heat and stir in the chopped parsley so its color and brightness are preserved; season to taste with Fine salt.
Let the salsa verde sit a few minutes for flavors to meld, then serve warm or at room temperature over fish, shellfish, grilled vegetables, or roasted potatoes.
