In a small saucepan over medium heat, melt butter and add oil. Add the onions and cook, stirring now and then until softened. Add the garlic, cook for a moment, then add in the peas and tarragon. Gently heat the peas through, stirring now and then, without letting them brown, until just done. (If you wish to garnish with some of the peas, remove a tablespoon or two now and set aside.)

Add the cream and bring to a simmer. Remove from heat and stir in about 1 1/2 tablespoons Parmesan cheese, reserving the remainder for garnish.

Add to a blender, covering the top with a towel and holding firmly, blend, stopping to scrape down as needed. Garnish with any reserved peas if desired and the remaining Parmesan.