Make the pear puree: In a small saucepan, combine the chopped pear, honey, and a sprig of rosemary with ½ cup of water. Cook on medium heat until the pears are soft (about 10 minutes).
Blend and strain: Remove the saucepan from heat and let the mixture cool slightly. Discard the rosemary sprig, and transfer the pear mixture to a blender. Blend until smooth. Strain through a fine mesh sieve to remove any chunks, leaving you with a smooth pear puree.
Combine ingredients: In a shaker, combine 2 tablespoons of the pear puree, pear juice, and lemon juice. Shake well to mix.
Add sparkling water: Fill a glass with ice cubes. Pour the pear mixture into the glass, then top with sparkling water. Stir gently to combine.
Garnish: Add a sprig of rosemary and a slice of pear to garnish. Serve immediately and enjoy!