Preheat oven to 425 degrees F (220 degrees C). Set a metal rack over a baking sheet.
Rub Cornish hens with olive oil; season inside and out with salt and pepper. Place 1 sprig rosemary in the cavity of each hen. Tie legs together with kitchen twine. Place hens breast side-up on the rack.
Roast hens in the preheated oven until an instant-read thermometer inserted into the thigh, near the bone, reads 165 degrees F (74 degrees C), 25 to 35 minutes.
Combine strawberry jam, white wine, balsamic vinegar, 1/4 teaspoon salt, and 1/8 teaspoon pepper in a small saucepan over medium heat. Cook and stir until jam starts to melt, about 3 minutes. Add Thai chile pepper; let steep for 5 minutes.
Remove sauce from heat and discard pepper. Serve alongside Cornish hens.