Preheat oven to 400 degrees.
In a heavy small saucepan on over medium heat, heat olive oil. Add shallot and sauté until shallot is transparent.
Add lemon zest, plum preserves and balsamic vinegar. Stir or whisk to combine and allow to simmer on low for 10 minutes until thickened (stirring periodically). Allow glaze to cool.
Allow glaze to cool.
While glaze is cooling, rinse hens and allow to drain with cavity facing down for 10 minutes. Pat dry inside and out with paper towels.
Liberally rub the salt and pepper inside and outside of the hens.
Stuff each hen with 2 quarters of Meyer lemon and 6 sprigs of thyme (note: I found bending the thyme in half and stuffing that into the hen’s cavity before the lemons worked well). Truss the legs in a crossed position, not too tight.
With a cooking/basting brush, brush hens on all sides with the glaze.
Place breast side up in a roasting pan or casserole. Wrap wing tips with a small piece of foil to avoid blackening if preferred. Place in warmed oven.
Set a timer for 50 minutes. Baste at 20 minutes with remaining glaze.
Check hens at 30 minutes. If having started to brown cover pan loosely with foil (the sugar in the glaze will cause the hens to blacken if left uncovered).
Baste finally at 40 minutes. Remove and check temperature at 50 minutes (hens should register 165 degrees on a meat thermometer placed between the thigh and breast).
Allow to sit 10 minutes before serving.