This not infrequent scenario is the subject of an interesting machloket. The Maharil[2] tells of one who started saying Asher Natan before the aliya and was corrected while in the middle of the beracha. The Maharil required him to revert to the beginning of the beracha, not just to the words “asher bachar,” where the two berachot diverge. Since he required the oleh to repeat HaShem’s name in beracha form (at the beginning of the beracha), he must have considered the beracha of Asher Natan before the aliya to be untenable, even b’di’eved.[3]
The Be’er Sheva[4] argues with the Maharil on two points. First, he reasons that if one starts a beracha improperly, he can and should correct it from the point of the mistake only, before its completion. The beracha is then valid because “everything follows its completion.”[5] Second, regarding one who finished the beracha improperly, the Be’er Sheva borrows a rule from the laws of the berachot of Kri’at Shema: the order of berachot is not crucial to their fulfillment.[6] Consequently, even if one said Asher Natan before the Torah reading and Asher Bachar afterwards, what is important is that the two berachot of an aliya were both recited. Thus, in your case, the Be’er Sheva would say to commence the Torah reading and have the oleh recite the normal opening beracha at the end.
The Eliya Rabba[7] agrees with the Be’er Sheva that one who realized his mistake in the middle of the beracha stops where he is and switches to Asher Bachar. In fact, he understands the Maharil to agree with the Be’er Sheva in this case. However, with regard to one who finished the beracha of Asher Natan, he agrees with the Maharil. He maintains that one cannot extrapolate from the berachot of Kri’at Shema to those of kri’at haTorah. The Beit Yosef[8] posits that despite their location, the berachot of Kri’at Shema are not really berachot for the purpose of Kri’at Shema. For this reason, even when one cannot fulfill the mitzva of Kri’at Shema, he still says those berachot. Accordingly, says the Eliya Rabba, the order of the berachot in relation to Kri’at Shema or to each other is not critical. In contrast, the berachot of kri’at haTorah were instituted for the kri’at haTorah, to be recited before and after the reading, and their order is critical. He compares switching the order of these berachot to saying Borei Nefashot before eating meat and Shehakol afterwards, and he cites the Avudraham’s explanation of why the wording of Asher Natan is appropriate specifically after the Torah has been read.
The Pri Megadim[9] says that since it is unclear whether the Be’er Sheva or the Eliya Rabba is correct, one should not say Asher Bachar after completing Asher Natan. This is because of the rule that if there is a doubt whether a beracha is necessary, one refrains from making it because of the concern of a beracha l’vatala.[10] The Sha’arei Ephrayim[11] counters with a pertinent point. If the oleh does not say Asher Bachar before the aliya, what will he say afterward? Saying Asher Bachar might be inappropriate after the aliya, in which case there is once again the concern of a beracha l’vatala. Thus, not making the correction before the aliya simply delays having to decide what to do about the doubt. In fact, the Sha’arei Ephrayim maintains that if one said only Asher Natan before the aliya, he probably should still say Asher Natan again afterwards.
Concerning the bottom line, since the Magen Avraham[12] and the Mishna Berura[13] agree with the Be’er Sheva¸ the standard p’sak is to commence laining the aliya after just Asher Natan and then to say Asher Bachar following the aliya. Only in a case in which the mistake was made after the aliya and Asher Bachar was recited a second time would we say that if he completed the beracha improperly, he must start again and make the correct beracha (Asher Natan), which was not yet recited.[14]