How to Make It
In a small saucepan, melt the butter over moderate heat until foaming. Add the anchovies and cook over moderately low heat until dissolved, about 2 minutes. Remove from the heat and whisk in the olive oil, vinegar and lemon juice. Add the thyme sprigs and let steep for 20 minutes. Discard the thyme and season the dressing with salt and pepper.
Meanwhile, in a small skillet, toast the bread crumbs over moderate heat, tossing, until golden, about 4 minutes. Let the bread crumbs cool.
In a large bowl, toss the spinach with half of the dressing and bread crumbs and season with salt and pepper. Transfer the salad to plates or a platter and top with the remaining bread crumbs and the shaved Parmigiano-Reggiano. Pass the remaining dressing at the table and serve with lemon wedges.
The bagna cauda dressing can be refrigerated overnight. Warm gently before using.
To make bread crumbs, tear 2 slices of day-old white bread into pieces, spread on a baking sheet and toast in a 300° oven until dried but not browned, about 10 minutes. Transfer to a food processor and pulse until coarse crumbs form.