Cut cauliflower into florets and place in a single layer on large rimmed baking sheet. Use 2 trays, if needed, so the cauliflower fits in one layer.
Drizzle cauliflower with olive oil and mix well, so oil is evenly distributed. Mix paprika with salt and pepper, sprinkle spice mixture over the cauliflower, and mix thoroughly. It's easier (and messier) to do this with your hands, but you could also use a large pair of tongs. Place cut sides down, where you can. The underside will crisp up when roasted.
Roast for 15-20 minutes, until crisp on the edges and tender inside.
Meanwhile, make dressing. In a small bowl, whisk together vinegar and mustard. Then add in spices and whisk. Cut shallot into small dice and whisk into mixture. Last, add in the oil and continue to whisk, until fully incorporated. Alternately, place all ingredients into a small jar with right fitting lid and shake vigorously until mixture is emulsified.
Place arugula in bowl and toss with 2 Tablespoons dressing. Arrange on a serving platter. No need to wash the bowl. Next add the roasted cauliflower to the bowl and toss with 1-2 Tablespoons dressing. Add cauliflower to the platter with arugula.
Notes
ARUGULA: If you can find fresh, large leaf arugula, BUY IT!! Use 1-2 bunches, depending on how big they are. Otherwise, buy 1 5-oz bag of baby arugula. Either way, you don't need to measure the 4 cups. Use as much as needed for the size of your crowd, or to fill the bottom of your serving dish. If you don't like, or can't find arugula, use spinach or another green. PEPPER: I prefer the slightly smoky flavor of white pepper over black pepper. Use what you have. Also, baby arugula doesn't have the same peppery flavor of full grown arugula....if you have full grown arugula, you may want to cut back on the amount of pepper in the recipe. MUSTARD: If you're making this for passover, omit the mustard. Add in some chopped fresh herbs, if you have some. MAKE AHEAD: Dressing will stay good in fridge for 2 weeks. Make it whenever it's convenient for you. Cauliflower can be made ahead and left room temp for several hours or place in the fridge for up to 5 days. It won't be crispy, but it will still be tasty! Bring to room temp before assembling salad. You could also gently reheat cauliflower in 400 degree oven for 8 minutes.