In a mixing bowl, whisk the citrus juices, shallots, garlic, cumin, cayenne, and honey together until combined. Slowly drizzle in the olive oil in a thin and steady stream until the dressing becomes emulsified. Taste and adjust with salt and pepper and set aside.
Pat dry and season peeled and deveined shrimp on both sides. In a large sauté pan over medium-high heat, add 1 tablespoon of olive oil to the pan, heat for a minute or so, and drop in the shrimp. Cook for about 1-2 minutes on each side until shrimp are pink and slightly fried. Take off heat and transfer to a large mixing bowl. Add the hominy and sliced tomatoes to the mixing bowl and pour in half of the vinaigrette. Toss to coat and let sit for a few minutes.
Meanwhile finely chop the cilantro, thinly slice the avocado, and crumble half of the cotija cheese. Add the prepped ingredients to the shrimp and hominy mixture and fold in the arugula. Pour in the remaining vinaigrette and toss to coat. Season the salad generously with kosher salt, pepper, and a squeeze of lime juice.
Transfer salad to a serving platter, sprinkle with the remaining cheese, and serve.