  Nodal lines are one-dimensional topological features of semi-metal band
structures along which two bands are degenerate as a result of non-accidental
symmetry-protected crossings, and behave topologically as $k$-space vortices in
the Berry connection. Here, we present a new class of tilted nodal lines,
protected by mirror symmetry, formed from the intersection of three band
crossings at a set of critical points. One crossing is gapped out, fusing the
remaining two crossings at the shifted critical points to form composite nodal
lines. We demonstrate these composite nodal lines are capable of supporting
fundamentally different Berry curvature textures than the typical two-band
case, despite having a simple ring topology. In addition, we present a
realistic model based on cubic, forced-ferromagnetic, EuTiO$_3$, where the spin
and orbital degrees of freedom are plentiful enough to allow the material
realization of such composite nodal lines. In this system, the composite nature
of the nodal line results in a spin Hall conductivity with a non-monotonic
dependence on carrier concentration.
