Fill a high-sided skillet with water to a depth of 1 inch. Add white wine, salmon, lemon, basil sprigs, and season generously with salt and pepper. Heat water over medium until almost simmering (but without bubbles breaking surface), then cover skillet. Gently cook salmon until just cooked through, 8 to 10 minutes.
While salmon cooks, place a steamer basket in a saucepan filled with 1-inch of simmering salted water. Layer potatoes then green beans in steamer basket and cook, covered, until potatoes are tender, about 10 minutes. Arrange salmon, beans and potatoes on a platter.
Whisk egg yolk in a medium bowl. Beginning with a few droplets at a time, drizzle olive oil into yolk while whisking vigorously (yolk will begin to lighten and thicken). Continue whisking and adding oil, whisking well to combine after each addition, until about half of oil remains. Increase oil additions to about 1 tablespoon at a time, whisking well to combine, until all oil is incorporated. Season with salt, pepper and remaining lemon juice. Thinly slice and stir in basil leaves. Serve mayonnaise on arranged platter.
Before her diagnosis, Caroline wrote a book on cakes called Cake Magic!. She started developing a birthday cake using her gluten-free mix found in that book. Check out other recipes she’s developing for her new life—and the stories behind them—on her blog, The Wright Recipes. Her next book, Catalan Food, written with chef Daniel Olivella, comes out in early September from Clarkson Potter.