How to Make It
In a large pot, melt 2 tablespoons of the butter. Add half of the minced shallots and all of the garlic and cook over moderate heat until softened. Add the Swiss chard and cook, tossing, until wilted. Transfer the chard to a colander and let cool. Press out as much liquid as possible and coarsely chop. Season with salt and pepper and press the chard into 6 patties; don't worry if they don't hold together.
In a small bowl, whisk the flour with the cornstarch and 1 teaspoon of salt. Sprinkle the mixture onto a work surface and set the chard cakes on top. Turn the cakes, pressing and squeezing them into compact patties and working in a little of the flour mixture as you go.
Spread the panko on a plate. Brush the tops of the cakes with mustard and invert them one at a time into the panko. Brush the bottoms with mustard and sprinkle panko on top; press to adhere. Transfer the cakes to a wax paper–lined plate and refrigerate until firm, about 20 minutes.
In a large skillet, melt the remaining 1 tablespoon of butter. Add the remaining minced shallot and cook over moderate heat until softened. Add the spinach and cook, tossing, until wilted, about 5 minutes. Transfer the spinach to a colander and press out as much liquid as possible. Return the spinach to the skillet. Stir in the mascarpone and season with salt and pepper. Keep warm.
Heat the olive oil in a large nonstick skillet. Add the chard cakes and fry over moderately high heat, turning once, until golden and crisp, about 6 minutes. Spoon the spinach onto plates and top with the chard cakes. Serve right away.