Using a food processor, blend the peas into a rough paste. Add the tarragon and lightly pulse for a few seconds, incorporating the herb but not fully breaking it down.

Transfer the mixture to a bowl and add the sugar. Mix until the sugar is fully incorporated. Cover and allow to rest for 2–3 hours, stirring periodically.

Place the mixture in a small saucepan and place over the lowest heat possible. Cook, stirring constantly, just until the sugar is dissolved. This should take less than 1 minute. Remove from the heat immediately and strain and discard the solids. Refrigerate the syrup until ready to use.