Place all ingredients for the basil pesto into a food processor and pulse until smooth. Season with salt and pepper.
Bring a large pot of water to a boil. Add perogies and cook stirring occasionally for 6 mins and drain.
In a large non-stick frying pan, heat canola oil over medium heat. Add perogies and fry until golden brown, 3-4 minutes per side.
In a large bowl, add perogies, tomatoes and cheese. Toss with pesto and serve on a large platter.