In a small bowl, whisk together all ingredients for aioli.
Heat a large skillet over medium-high heat for a couple of minutes. Season salmon with salt and pepper on both sides. Add oil to skillet. Once it starts shimmering, add the salmon (skin-side down if it has skin). When first side releases easily (about 2-3 minutes), flip and continue cooking on other side until barely cooked through, about 1 minute more (it will continue cooking off of the heat). It should be flakey and nearly opaque in the thickest part.
Divide aioli between buns, spreading evenly on both cut sides. Divide salmon among buns, and top with a small handful of pea sprouts, and several slices of cucumber.