To make the vinaigrette, add olive oil to a small bowl and whisk in diced jalapeño, lemon or lime juice, and salt and pepper. Let sit at room temperature while you make the hummus so the flavors infuse.
In a blender, add canned chickpeas, ice water (no ice), tahini, lemon juice, and whole garlic cloves. Blend on medium until smooth, adding more cold water to make it smoother if necessary. Add 1 tbsp of salt (or more to taste) and blend one more time to combine.
To plate, spread the hummus in a shallow bowl or plate. Drizzle the vinaigrette over the hummus and sprinkle with paprika and sea salt if desired.
Hummus will last up to 1 week in the fridge.