Heat a saucepan over medium heat. Once hot, add the oil, butter, shallot, and garlic. Saute until golden brown. Then place in a blender or food processor with the peas and lemon juice.
Blend until smooth, add broth a teaspoon at a time to thin out the puree so its manageble to blend. (You dont want to add too much broth at once or it will become too watery)
Season with salt and pepper to taste. Let sit at room temperature until ready to serve.
Notes
Pro Tip: Puree the peas while still frozen, this will give the puree more body. The friction from the blender will provide heat as well as letting it sit out at room temperature before serving so its not being served cold.