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In a small saucepan of boiling salted water, cook the pearl onions until just tender, about 3 minutes. Drain and trim the onions, then squeeze them from their skins.
In a large skillet, melt the butter in the 2 tablespoons of olive oil. Add the sliced onions and thyme, cover and cook over moderately low heat, stirring a few times, until softened, about 7 minutes. Add the garlic and cook over moderate heat until fragrant, about 2 minutes. Add the pearl onions and wine and cook over moderate heat until the wine has reduced by half, about 3 minutes. Add the broth and simmer until reduced by one-third, about 4 minutes. Remove from the heat, stir in the mustard and parsley and season with salt and pepper. Cover the skillet and keep warm.
Heat a griddle over two burners. Add enough olive oil to lightly coat the griddle. Cook the ham steaks over moderately high heat until browned on the bottom, about 3 minutes. Turn and cook until heated through, about 1 minute. Transfer the ham to plates, top with the onion mixture and serve.
The onion mixture can be refrigerated for up to 2 days.