  For more than a century, the Painlev\'e I equation has played an important
role in both physics and mathematics. Its two-parameter family of solutions was
studied in many different ways, yet still leads to new surprises and
discoveries. Two popular tools in these studies are the theory of isomonodromic
deformation that uses the exact WKB method, and the asymptotic description of
transcendents in terms of two-parameter transseries. Combining methods from
both schools of thought, and following work by Takei and collaborators, we find
complete, two-parameter connection formulae for solutions when they cross
arbitrary Stokes lines in the complex plane. These formulae allow us to study
Stokes phenomenon for the full two-parameter family of transseries solutions.
In particular, we recover the exact expressions for the Stokes data that were
recently found by Baldino, Schwick, Schiappa and Vega and compare our
connection formulae to theirs. We also explain several ambiguities in relating
transseries parameter choices to actual Painlev\'e transcendents, study the
monodromy of formal solutions, and provide high-precision numerical tests of
our results.
