If you have a GRBL controller, enable ‘Flood Fill’ for that layer and it will take care of it. If you have a DSP controller, the flood fill option is not available because it produces motion paths that confuse them, so I’m working on fixing it.
A good solution that works for both is to split the shape manually using the boolean tools. First, group the inner and outer curve of your oval so it’s one object. Then draw a shape that splits your oval down the center, and surrounds one side, using the pen tool, like this:
Select both shapes and duplicate them (Ctrl-D) so you have two copies of each. Then, select one of the ovals and one of the rectangles and click the boolean subtract button to remove the area of the rectangle from the oval.
Then select the remaining oval and the remaining rectangle, and click the boolean union, which keeps the area that overlaps. I did these two steps side by side so you can see the result, but you would just do them in place:
When you do it in place, you get this:
If you set that layer to fill shapes individually, or fill by groups, instead of filling everything together, you can fill each side separately: