We start by evaluating $(1\nabla 2)$.
Using the given operation, we have $1\nabla 2 = 2 + 2^1 = 2 + 2 = 4$.
Now we evaluate $(4\nabla 3)$.
Using the given operation, we have $4\nabla 3 = 2 + 3^4 = 2 + 81 = 83$.
Therefore, the value of $(1\nabla 2) \nabla 3$ is $\boxed{83}$.
The answer is: 83
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Define the operation $a\nabla b = 2 + b^a$. What is the value of $(1\nabla 2) \nabla 3$?

### Answer:
