Heat oil in a large skillet over medium-high heat. Add beans and shallot and cook, stirring occasionally, until the shallot starts to soften, 1-2 minutes.
Sprinkle both sides of cod with salt and pepper. Spread the beans into a flat layer in the pan and gently place the cod on top. Increase heat to high, add broth, cover and cook until the fish is just cooked through, 4-6 minutes.
With a slotted spoon, transfer the cod and beans to a large serving plate, cover to keep warm. Cook the broth over high heat, uncovered until reduced to about 1/2 cup, about 5 minutes. Remove from heat and stir in pesto. Pour the sauce over the fish and beans and serve with lemon wedges, if desired.
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