We report the discovery of a kpc-scale lacy filamentary structure in low surface-brightness H$α$ and [OIII]$\lambda5007$ emission around the low-redshift, extremely metal-poor and compact reionisation-era analogue SDSS J1044+0353. We identify seven elliptical arcs in H$α$ emission at $\mathrm{SB}_\mathrm{Hα} \sim 1 - 2 \times 10^{-18}$erg s$^{-1}$cm$^{-2}$arcsec$^{-2}$. We interpret these features as limb-brightened giant-shells that bound egg-shaped super bubbles with 3-3.5 kpc radii. These shells are significantly larger than the known giant shells around nearby star-forming dwarfs. Kinematic maps reveal a gradient perpendicular to the major-axis and line broadening in the outskirts. The latter, when interpreted due to line-splitting of the expanding shells, suggests expansion velocities of $\sim 40$km s$^{-1}$. Notably, the properties of the giant shells evade description by simple analytic prescriptions for energy- and momentum-driven super-bubbles.