Bring a large pot of salted water to a boil.
Add the frozen pierogi and broccoli florets and cook until the broccoli is crisp-tender and the pierogi float to the surface, about 5 minutes.
Drain everything well in a colander.
While the pierogi cook, heat 2 tablespoons (30 ml / 1 fl oz) of the olive oil in a large skillet or frying pan over medium heat.
Add the chopped onions, cover the pan, and cook until softened and translucent, about 5 minutes.
Uncover the skillet and stir in the walnut pieces and red pepper flakes.
Cook for about 1 minute, stirring constantly, until the walnuts are fragrant and lightly toasted.
Add the drained pierogi and broccoli to the skillet. Gently toss and cook, allowing the pierogi to get lightly browned and golden on both sides, about 5 minutes.
Season generously to taste with salt and freshly ground black pepper.
Drizzle with the remaining 1 tablespoon (15 ml / 0.5 fl oz) of olive oil and serve immediately.
Don't overcrowd the pan when browning the pierogi. Use a large skillet and work in batches if necessary to ensure they get a nice golden-brown crust.
