Few verses in the Hebrew Bible have troubled readers as much as the one that says God hardened Pharaoh's heart. Targum Pseudo-Jonathan on Exodus 11:10 offers a subtle reading: the Lord "strengthened the design of Pharoh's heart." The word design does the work. God does not implant resistance where none existed. God reinforces the architecture Pharaoh has been building all along.
In the Aramaic, the verb atkaf (strengthen) sits beside machshavta (design, plan). Pharaoh already had a plan. That plan was to enslave, to dominate, to refuse. God's role, in the Targum's reading, is to make sure Pharaoh does not lose his nerve halfway through, the way lesser tyrants do when disaster starts arriving. A Pharaoh who caves after three plagues teaches nothing; a Pharaoh who holds out for ten becomes the backdrop against which the glory of the Exodus is revealed.
The rabbis often noted the problem this raises for free will. If God reinforced Pharaoh's resolve, is Pharaoh still responsible? The Targum's phrasing answers by pointing to agency. The design was Pharaoh's own. God strengthened the thing Pharaoh had already chosen to build.
Meanwhile, Moses and Aaron have performed every sign asked of them. The verse lists them by name as if to contrast their obedience with Pharaoh's reinforced stubbornness. Two prophets say yes to every task. One king says no to every offering of mercy.
Takeaway: A hardened heart is usually a heart that has been building its walls for years. God only holds them up when the builder is already finished.