Begin the brown butter hollandaise: In a small, heavy-bottomed saucepan over medium heat, add the butter. Cook, swirling the pan constantly, until the butter is golden brown and smells nutty, about 5 minutes. Transfer to a small bowl to cool slightly.
Meanwhile, make the mignonette: In a small bowl, combine the red wine vinegar and shallot; season with a pinch of salt and pepper and set aside.
In a blender, add the white wine vinegar, 1⁄4 teaspoon kosher salt, and the egg yolks. With the motor running, trickle in the brown butter very slowly, leaving behind the browned solids (discard the solids). Continue blending until all the butter has been added and the mixture is thickened and creamy. Transfer to a bowl, and whisk in up to 1 tablespoon of water as needed to thin hollandaise to the consistency of loosely whipped cream.
Prepare the oysters: In a small skillet over medium-high heat, melt the butter. Once foaming, add the spinach and cook, stirring occasionally, until wilted, about 2 minutes. Remove and set aside.
Preheat the broiler and line the bottom of a baking sheet with aluminum foil. Meanwhile, shuck the oysters, leaving the meat and juices in the bottom shell. Transfer to the prepared baking sheet, scrunching up the foil beneath the shells or tucking the top shells under the bottom shells as needed to keep them level. Top each oyster with some of the spinach leaves, a few pieces of diced chorizo, and a generous spoonful of hollandaise.
Broil until the hollandaise is lightly browned, 2-3 minutes. Remove and serve immediately with the mignonette.