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Preheat oven to 400 degrees F.
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Slice any large potatoes in half lengthwise. Toss potatoes with 1 tablespoon olive oil, 3/4 teaspoon salt, and 1/4 teaspoon pepper. Place potatoes on a baking sheet.
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Roast until golden brown and tender, about 30 to 35 minutes, tossing once during roasting. Use a heavy spatula to lightly flatten (smash) potatoes.
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Make the dressing while the potatoes are roasting.
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Thinly slice 1 jalapeño pepper (using a mandoline recommended). Place jalapeño slices in a large bowl.
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Seed and mince remaining jalapeño pepper. Place in a blender along with lime juice, sherry vinegar, onion, garlic, honey, mustard, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Blend on high speed until liquefied.
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Reduce blender speed to low and slowly pour in remaining 1/4 cup olive oil.
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Place smashed potatoes in the bowl with jalapeño slices. Add parsley.
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Pour dressing on top. Gently toss to combine (potatoes are soft so be careful or they will break apart). Allow to sit 10 minutes before serving for potatoes to soak in dressing. Serve warm or at room temperature.