Heat enough olive oil to fully cover the base of a large pan with high sides or dutch oven over a medium-high heat. Add half the mushrooms and a pinch of salt and cook for about 3 to 4 minutes (stirring only a couple of times) until seared and golden. Transfer to a plate and repeat with the other half of the mushrooms.
In the same pan, heat another glug of olive oil and place over a medium-low heat. Add onion and cook for 4 to 6 minutes, stirring occasionally, until softened.
Add tomato paste and cook stirring for 30 seconds. Add garlic and thyme and cook for another 30 seconds.
Add wine, bring to a boil, and cook for about 2 to 4 minutes, until reduced by about half.
Add vegetable broth and the cooked mushrooms along with any of their juices to the pan. Reduce heat to medium-low and simmer for about 18 to 22 minutes, stirring occasionally. The broth should have reduced significantly and you should have thickened, stew-like mushroom sauce when it’s done cooking.
While the mushrooms are simmering, warm your peas in a medium saucepan with 1 cup boiling water for 1-3 minutes until completely thawed and bright green. Drain peas and combine with a generous pinch of salt and butter or olive oil in a food processor or blender and puree until smooth-ish (some chunks are a-okay).
Serve warm green pea mash in bowls topped with mushrooms, toasted pine nuts (or walnuts), and parsley.