Cut 6 tablespoons butter into cubes and refrigerate. Melt 2 tablespoons butter in a saucepan over medium-low. Add onion, sliced garlic, shiitake stems, tomato, black peppercorns, and bay leaf; cook until vegetables are soft, about 12 minutes. Add balsamic vinegar and 1/3 cup water; cook until syrupy, about 4 minutes.
STEP 2
Reduce heat to low; add cubed butter, whisking thoroughly. Season sauce with salt and pepper. Strain into a bowl and keep warm over a double boiler.
STEP 3
Heat 2 tablespoons olive oil in a skillet over high heat. Add spinach; cook until wilted, using a fork with garlic clove. Season and drain.
STEP 4
Wipe skillet clean. Reduce heat to medium; add 3 tablespoons butter and shiitake caps. Cook until softened, then stir in corn kernels; heat through. Season and keep warm.
STEP 5
Increase heat to high; add remaining butter and olive oil. Season salmon strips; cook until browned but barely cooked through, about 3 minutes per side.
STEP 6
Divide spinach among plates; surround with corn and shiitakes. Place a salmon strip on top; spoon sauce on fish. Garnish with chives; serve immediately.