Combine the lemon juice, water and sugar in a small saucepot over medium high heat. Bring to a boil, then reduce to a simmer until the sugar has dissolved, about 7-10 minutes.

Toss into the blender with the mint and puree until very smooth.

Transfer everything to a contain and allow to cool in the fridge until very cold, at least 2 hours.

When ready to process in the ice cream maker, strain the mixture through a chinois and into the prepared ice cream maker. Process according to manufacturers instructions, then transfer to a container and freeze until frozen.

Heat a large stockpot over medium high heat with the butter and oil. Add in the onion, and garlic and stir until softened, about 4 minutes.

Add in the peas, and stock, cover, and allow to cook until the peas are warmed through and slightly softened, about 10 minutes.

Remove from the heat, then add in the mint leaves.

Transfer to a blender and puree until very smooth (you will likely need to do this in batches). You can add a little of the cream to help it along if needed.

Strain the pea mixture through a fine chinois to discard of the pea pulp (you can eat this separately, it's very tasty) and into a large bowl.

If you haven't already used all of the cream, add the rest now (or to your own discretion if you want a lighter soup). Then season with salt and pepper to taste. Cover and refrigerate until very cold, at least 2-3 hours.

When ready to serve, ladel some of the soup into bowls.

Add a dollop or two of creme fraiche.

Create a quinelle of sorbet by scooping it up with a big spoon, then scraping it out of the spoon with another spoon and repeating back and forth until you get a oval like shape. Drop on top of the creme fraiche.

Garnish with a few fresh pea shoots.