Challah in chutz la'aretz may be taken after (most of) the bread has been eaten, since it is only mid'rabonon (Shulchan Aruch YD 323:1). However, one must leave over a little more than the shiur challah which he will separate, in order that there should be something leftover from which to separate it (Rema ibid).
Why is there no problem that the taste of the bread (before chala was taken) will be in the oven tray?
Rema (YD 324:12, quoting the Beis Yosef s.v. מצאתי) writes:
הָאוֹפֶה פַּשְׁטִידָ''א מֵעִסָּה שֶׁלֹּא הֻרְמָה חַלָּתָהּ, וּבְתוֹכוֹ בָּשָׂר, מֻתָּר לְהַפְרִישׁ מֵעִסָּה אַחֶרֶת הַחַיֶּבֶת בְּחַלָּה עַל זוֹ
וְנִפְטַר גַּם כֵּן טַעַם הָעִסָּה הַנִּכְנָס בַּבָּשָׂר
Thus, separating challah at a later point exempts any absorbed taste from the dough.
(credit: Double AA)