Stir together the mayonnaise and paprika in a small bowl until smooth. Sprinkle the flank steak with salt and pepper, then evenly spread the paprika mayonnaise on top of the meat. Set aside for 15 minutes.
Meanwhile, toast the coriander and cumin seeds in a medium skillet over medium heat until fragrant, about 2 minutes. Transfer to a bowl to cool, then pulse in a spice grinder until finely ground and return to the bowl. Toast the cashews and pistachios in the same skillet, stirring occasionally to prevent burning, until browned, about 5 minutes. Add the nuts to the bowl with the toasted ground spices; add the red pepper flakes and toss to combine. Toast the sesame seeds in the same skillet until fragrant and browned, about 3 minutes. Add to the spiced nuts.
Position a rack about 6 inches from the heat source and preheat the broiler to high.
Set a broiler pan or a heavy baking sheet under the heating element and preheat for 5 minutes. Carefully remove the hot pan and spray with cooking spray or brush lightly with oil and quickly put the meat on the pan. Broil until a thermometer inserted sideways into the thickest part of the meat reads 130 to 135 degrees F and the paprika-mayonnaise coating is deep brown and bubbly, 5 to 7 minutes. Remove from the broiler and let the steak rest for 5 minutes before slicing.
Slice the meat thinly against the grain. Stir the mint into the spiced nuts and scatter some nut mixture on top of the steak. Put the rest of the spiced nut mixture in a bowl to serve on the side for sprinkling. Garnish the steak with additional mint leaves if using.
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