For the simple syrup, peel and chop the pear and ginger. The pear should be cut into 1" or less squares. For the ginger you only need a 1" piece. I like to slice it in half or thirds to impart more flavor.
Combine water, honey, pear, cinnamon and ginger in a small sauce pan. Bring to a simmer over medium heat. Stir until honey dissolves. Reduce heat and simmer for 5 minutes. Take off the heat and allow to cool for 10-15 minutes. Strain and discard the solids. Refrigerate until chilled and ready to use.
Combine bourbon, pear nectar, simple syrup, and lemon juice in a cocktail shaker with ice. Vigorously shake until chilled.
Divide between two martini glasses and garnish with a slice of pear and sprig of rosemary for garnish.
Notes
You can serve this cocktail over ice in a lowball glass if you'd like.
Try to find pear nectar for this cocktail, but if you can't find it you can use pear juice instead.