Place pie crust in pie pan and use a fork to poke vent hole in it along the bottom and on the sides. Place in oven for 15 minutes.
While pie crust is in the oven, slice or chop tomatoes and place in colander, in kitchen sink or sitting atop of large bowl. Use back of spoon to press on tomatoes and squeeze out excess juice. Allow tomatoes to continue to drain in colander until ready to use. Discard juice.
Remove crust from oven and evenly distribute onions along bottom of crust. Next, evenly spread tomatoes and basil over top of onions.
Combine shredded cheese and mayonnaise in small bowl and mix together until thoroughly combined. Then, evenly spread over the top of the pie filling.
Place in oven for another 40 minutes, or until crust is golden brown. Garnish with additional chopped basil if desired.