How to Make It
Heat 1/2 lb. butter and 2 cups canola oil in a 4-qt. saucepan over medium heat until butter melts. If potatoes are differently sized, halve the larger ones so they all cook at the same rate. Add potatoes to butter-oil mixture, which should just cover them (add a little more canola oil if necessary). Reduce heat to low and cook, covered, until potatoes are tender, 25 to 35 minutes depending on size.
While potatoes are cooking, make Meyer lemon vinaigrette: Whisk together lemon juice, olive oil, 1/4 tsp. salt, and a couple of pinches of white pepper. Set aside.
Transfer potatoes to a plate using a slotted spoon. Reserve 2 tbsp. butter-oil mixture and save the rest for another use (it freezes well). Season potatoes with 1/2 tsp. salt and let cool.
Bring a medium pot of salted water to a boil and fill a medium bowl with ice and cold water. Shuck corn, then cut kernels from cob (stand the cob in a bowl on its narrow end and slice downward with a sharp knife). Add kernels to boiling water. Cover pot. When water returns to a boil, blanch kernels 20 seconds, drain in a fine-mesh colander, and pour into ice water. As soon as kernels are cool, drain again.
Heat a (not nonstick) frying pan over medium-high heat. Swirl in remaining 2 tbsp. canola oil. Add chanterelles, season with 1/4 tsp. each salt and white pepper, and sauté until tender, 5 to 7 minutes. Transfer to a bowl.
Gently smash cooled potatoes between your fingers and thumbs. Reheat pan over medium-high heat, swirl in 2 tbsp. reserved butter-oil mixture, and add smashed potatoes. Sauté until golden brown, 10 to 15 minutes. Stir in shallot and garlic and cook, stirring constantly, 30 seconds. Transfer crisp potatoes to a serving platter.
Pour white wine into pan, let sizzle a minute, and add chicken stock. Cook over medium-high heat until liquid is reduced to about 1 cup, about 10 minutes.
Stir in remaining 2 tbsp. butter. Add cooked corn and chanterelles, season with salt, and heat through, about 2 minutes. Stir in minced parsley. Spoon corn mixture over potatoes.
Toss pea shoots with Meyer lemon vinaigrette and mound over vegetables. Add spoonfuls of ricotta, plus a few sprigs of flowering thyme if you like.
For the recipe to be gluten-free, use gluten-free stock.