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Assume I have a list of plaintext text and its corresponding ciphertext which was created using a specific key with AES in ECB mode.

Can I recover that key?

If, how big does the list of plaintext and matching ciphertext have to be to be able to find it in a feasable amount of time (say in 1 or 2 hours)?

Assume I have a list of plaintext text and its corresponding ciphertext which was created using a specific key with AES in ECB mode.

Can I recover that key?

No. This is what is referred to as a known plaintext attack, and secure block ciphers are designed to prevent exactly this kind of attack. This answer on the Mathematics Stack Exchange goes into more detail about the notion of IND-CPA ("indistinguishability") which AES is conjectured to meet and how that implies that a known plaintext attack is impossible.

What is the simplest attack is the Brute Force Attack. However, it is infeasible to brute-force even AES-128 bit, AES also supports 192, and 256-bit keys sizes. To break the AES-128 with brute force, you need to execute $2^128$ AES operations, today's top computers can reach $2^63$ around one hour.

In brute-force, the number of elements in your list is not important. The problem is the key-size. You have to check every possible key to match one of your plaintext-ciphertext pair;

for each k in possible keys
 if E(k,P1) == C1
 testWithSomeOtherPair(k)

Once you found you can verify with the other plaintext-ciphertext pairs.

Note: there are other types of attacks (related-key attacks) faster than the brute-force for AES-192 and AES-256 with $2^176$ and $2^99.5$-time, respectively. But they are still infeasible to reach. For AES-128, the fastest known is the Biclique attack with $2^126.2$ and that is still infeasible and in practice, the brute-force may still beat the Biclique attack which requires $2^88$-data and $2^8$-memory. Biclique attack for AES-192 and AES-256 runs with $2^189.7$ and $2^254.4$ computational complexity, respectively.