Fill a stockpot three quarters of the way full with water. Season generously with 2 tbsp of kosher salt, or the measurement of salt according to the box. Heat on high and bring the water to a boil.
Place a large, deep skillet on a burner that's set to medium heat. Season with 1-2 tbsp of olive oil, then add the pimentos. Season with a pinch of salt and stir.
Add the pasta to the boiling water and cook until 2 minutes before the box says it's al dente. One minute before you reach 2 minute before al dente, add the green beans to the pot and blanch for 1 minute.
Transfer the pasta and green beans to the pot with the pimentos. Stir together.
Adjust the heat to low. Add the vegan cheddar and 2 tbsp of vegan mayo. Toss together until melted and combined. If the cheese and mayo are too sticky and not *saucy,* add about 1 tbsp of pasta water and continue mixing until nice and saucy. Add the tomato paste and stir to combine. Taste to make sure you like flavor. TASTING NOTES: If you want more sweetness, add more tomato paste. If you want more pimentos, add more. If you want more saltiness, add more vegan cheddar OR more pasta water. Don't make it super salty because the rest of the mayo is coming in later. Transfer the pasta to a large bowl. If serving quickly thereafter, put the bowl in the freezer for 15 minutes to bring the temperature down. If serving the next day or in 2 days, just cover and refrigerate until you're ready to serve.
Right before serving, add 3 more tbsp of mayo and mix. Add dill and cherry tomatoes and combine until all ingredients are evenly spread thorughout. If you would like the pasta salad to be creamier, add more vegan mayo to your taste, preferably 1 tbsp at a time. Enjoy!!