Mince the shallot, chop the herbs, juice the lime(s), then place each in a standard-sized mason jar. Sprinkle in the paprika and pour in the olive oil. Add a few pinches of kosher salt and about 5 grinds of fresh black pepper. Seal the jar and shake vigorously to combine everything. Taste and adjust the flavors as desired (a little more lime, more salt, etc).
Prepare the kohlrabi by cutting off the root end, then cutting the kohlrabi bulb into four quarters. Use a Y-shaped vegetable peeler to peel off the thick outer skin of the kohlrabi, then use a mandoline, sharp knife, or that same Y-shaped vegetable peeler to shave paper thin slices of the kohlrabi.
In a large serving bowl, toss together the kohlrabi slices and about half of the lime-paprika dressing. Let the kohlrabi sit in the dressing (in the fridge or at room temperature) to allow it to soak up the flavors and soften.
Meanwhile, toast the pecan halves in a 300 F oven or in a skillet for about 8-10 minutes, until fragrant. Set aside to cool, then chop roughly.
Add the chopped pecans and arugula to the bowl with the dressed kohlrabi. Toss everything together, taste, and season with a little extra salt/pepper if needed. Pour a little more of the dressing in (this salad should be well dressed), then serve immediately.