Preheat your broiler.
Cook the linguine in a large pot of boiling, lightly salted water according to package directions.
Before draining, use a ladle to reserve 1/2 cup (480 ml) of the starchy cooking water.
Drain the pasta, return it to the hot pot, cover, and set aside to keep warm.
While the pasta cooks, prepare the garlic toasts.
In a small bowl, combine 1 tablespoon (15 ml / 0.5 fl oz) of the olive oil with about 1 teaspoon of the minced garlic.
Brush this mixture onto the cut sides of the English muffins.
Place the muffins on a baking sheet and broil 3 to 4 inches from the heat for 2 to 3 minutes, or until golden and toasted.
Sprinkle with 1 tablespoon (15 ml / 0.5 fl oz) of the snipped basil and set aside.
To make the sauce, heat the remaining 2 tablespoons (30 ml / 1 fl oz) of olive oil in a large saucepan or skillet over medium-high heat.
Add the remaining minced garlic, the rest of the 3/4 cup (960 ml) of basil, and the halved cherry tomatoes.
Cook for 2 minutes, stirring occasionally.
Pour in the reserved 1/2 cup (480 ml) of pasta water and the sugar.
Continue to cook for 3 to 4 minutes more, until the tomatoes have softened and started to break down.
Season to taste with salt and pepper.
Add the cooked pasta and halved kalamata olives to the saucepan with the sauce.
Stir everything together to combine and allow it to heat through for about a minute.
Serve immediately, garnished with a sprinkle of vegan Parmesan cheese and extra fresh basil, if desired.
Serve the toasted garlic muffins on the side.
Add a pinch of red pepper flakes with the garlic in step 3 for a gentle, warming heat.
Don't skip reserving the pasta water! The starches in the water are essential for creating a silky sauce that clings perfectly to the linguine.
