In a large shallow wide pan, heat 2 tablespoons olive oil over medium heat. Add the thyme, shallots, and garlic. Add the wine and cover with a lid; then add the chicken stock and re-cover. Place the clams and mussels in the pan and cover with the lid to steam them.
It should take about 3 minutes for the clams and mussels to open. When they open, remove them from pan onto a flat tray and allow to cool. Increase the heat to reduce the remaining liquid in the pan by half and then turn off the heat. Remove the clams and mussels from their shells and return them to the reduced cooking liquid.
Meanwhile, slice the mushrooms and heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add mushrooms and saute until golden brown. Season to taste with salt and pepper. Remove from heat and stir in the chopped chives.
To serve, reheat the clams and mussels in the reduced cooking liquid. Divide among 4 deep bowls. On top of each, place a small pile of mushrooms. Toss the salad greens in walnut vinaigrette, and place a small bouquet of salad on top to complete.
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