In a large bowl, mix together the cream cheese, ½ cup mayonnaise, Worcestershire sauce, smoked paprika, garlic powder, and Tabasco until smooth.
Add in the freshly shredded cheddar cheese, Monterey Jack cheese, drained pimentos, and grated onion. Stir until evenly combined and taste for seasoning. The pimento cheese will firm up in the fridge, so add more mayonnaise as needed to reach your desired texture.
Chill the dip for 30 minutes to allow the flavors to meld, then transfer to a serving dish and enjoy with crackers, crudités, or in sandwiches.
If serving later, store the pimento cheese in an airtight container and refrigerate for up to 5 days. Allow to come to room temperature before serving.