Add one stick of butter, shallot, and garlic to a skillet over medium-low heat. Allow the butter to melt and the shallot and garlic to become fragrant and tender, stirring often so the garlic doesn't burn.
When butter is fully melted, add Worcestershire sauce, Dijon mustard, hot sauce, minced onion, paprika, lemon zest, and juice of half the lemon. Stir well to combine. When all cowboy butter ingredients are fully incorporated, add half of the melted butter to a small bowl and refrigerate until ready to use.
Add raw shrimp to a large bowl. Season with Shake That All Purpose Seasoning (or substitute your favorite all-purpose seasoning or salt and pepper). Toss raw shrimp in a large bowl with the other half of the melted butter to coat evenly.
Heat griddle (or large skillet) over medium heat. For griddle cooking, griddle temperature should be about 375-400℉.
Add the shrimp to the heated cooking surface. Cook on the first side for 2-3 minutes, or until about halfway cooked through. Then flip to the second side and continue to cook until done, about another 2-3 minutes.
When shrimp are fully cooked, remove from the griddle and transfer to a serving platter. While hot, top with the rest of the refrigerated cowboy butter (if desired). *For a lighter dish, you do not have to add the additional half of the compound butter. You can wrap the leftover butter in plastic wrap tightly in a log shape, and save it for steak, fish, etc.
Squeeze a bit more lemon juice on top of the shrimp if you wish. Serve immediately.