Line a 8½ × 4½-inch or 9×5-inch loaf pan with parchment paper; grease parchment.
Bring butter, cream and rosemary to boil. Remove from heat and stir in ¼ teaspoon salt; let cool.
Combine water, corn syrup and sugar with a wooden spoon or heat-proof rubber spatula in a large saucepan. Stir until sugar is saturated with water.
Bring sugar solution to a boil over medium-high heat, and cook, without stirring, until sugar has dissolved and temperature reaches 300°F (149ºC), about 10 minutes. Reduce heat to medium and simmer, gently swirling pan, until edges of mixture start to turn a light amber and temperature reaches 320ºF (160ºC) to 325ºF (163ºC), about 5 minutes.
Once 320ºF (160ºC) is reached, remove from heat. Remove and discard rosemary sprig from cream mixture; carefully pour a quarter of the cream mixture into sugar syrup and swirl to incorporate. (Be careful, mixture will bubble up.)
Add remaining cream and butter mixture and stir to incorporate. Return pan to medium-high heat and cook, stirring frequently, until caramel reaches 240°F (115ºC) for softer caramels or 245ºF (118ºC) for chewier caramels, 5–10 minutes.
Carefully pour caramel into prepared pan; allow caramel to cool for 20 minutes at room temperature, then sprinkle with ½–1 teaspoon sea salt and let cool until completely solid and cold to touch, 1–2 hours.
Pull edges of parchment paper to release caramel from pan. Cut caramel into ¾-inch-wide strips and then crosswise into 1-inch pieces. Individually wrap pieces in waxed-paper squares, twisting ends of paper to close.
Caramels can be refrigerated for up to 3 weeks.