Pre-heat oven to 450 degrees, and line a rimmed baking dish with parchment paper.
Wrap each quail in 2 pieces of bacon, securing with toothpicks.
In a small saucepan, melt together the pesto and butter. Stir until well melted and fully mixed.
Place bacon-wrapped quail in the baking dish. Drizzle each with a spoonful of the pesto sauce, leaving the remaining sauce for gently garnishing at serving time.
When the oven is fully up to temperature, bake quail for 20 minutes.
Turn quail over in the baking dish, then return to oven and BROIL for about 3 minutes, or until bacon is getting brown, crackly, and crispy.
Turn quail back over (so the side that was up as they baked is now back on top), and broil for about another 3 minutes, until bacon is brown and crackly on this side as well.
Remove from oven, and serve as soon as possible. Use the remaining butter pesto sauce to drizzle each quail as it's plated.
If you're a passionate pesto lover, consider doubling the sauce recipe, and serving the remaining sauce in a small ramekin at the table.