Hello Gary,
you need to perform some configuration to take advantage of both links.
There are two ways of doing this:
a) move the eBGP session to loopback addresses and with two static routes on each router with destination the neighbor router's loopback address
b) define a second eBGP session on the physical ip addresses of both routers and add the command maximum-paths 2 under router bgp x on both routers
a) config
R1
int loop1
ip address 1.1.1.1 255.255.255.255
desc ebgp loop
!
router bgp X
neighbor 2.2.2.2 remote-as y
neighbor 2.2.2.2 update-source loop1
neighbor 2.2.2.2 ebgp-multihop 2
!
ip route 2.2.2.2 255.255.255.255 s0/0
ip route 2.2.2.2 255.255.255.255 s0/1
the same must be done on the second router define loop1 wiht ip 2.2.2.2/32 add static routes for net 1.1.1.1/32 uing the links define in the same way the eBGP session
b) config
nothing special
config a has to be preferred because only one copy of each advertisement is received for example when you receive a full BGP internet table.
note: in this case you see only one route for each prefix but there are two routes for the eBGP next-hop and recursion provides load-balancing.
config b uses the maxim-paths and in this case you see two B routes for each prefix in the routing table.
Hope to help
Giuseppe