In a large bowl, stir together water, salt, and sugar until fully dissolved.
Add shrimp and refrigerate for 30 minutes.
Drain and pat shrimp dry with paper towels.
In a food processor, blend garlic cloves and soy sauce until smooth.
Stir the garlic-soy mixture into softened butter until fully combined.
Set aside (refrigerate if making ahead, then soften before use).
Heat the griddle to medium-high (375°F–425°F).
Lightly coat with oil.
Place shrimp on the griddle in a single layer.
Sear undisturbed for 1–2 minutes, then flip.
Add 3–4 tablespoons of garlic butter and toss to coat.
Optional: Splash with soy sauce and cook 2–3 more minutes until opaque and slightly charred.
Remove from heat and serve immediately.