Growing large beets
The most success I have had with growing large beets, and this is true for all root crop, is to make sure you have thinned them when their true leaves come in. Thinning them with 1-2 inch spacing allows root to size up and allows air flow through the leaves to promote growth.
I don't start beets indoors for a couple of reasons. Roots do not like to be transplanted. Starting them indoors takes up space that could be used for warm weather fruiting crops. Direct seeding beets allows you to maximize spacing, yield and can be started after first frost AND in August for fall crop. I have much success seeding beets early-mid August. A good rule of thumb is to have your fall roots seeded by Aug 15. You could potentially extend this past mid August if you plan on using row cover.
Peas are particular about their environment. Grow in late spring to early summer with 5 to 6 hours of sun, lots of water and very loose soil (only compost, sand, worm castings). Fertilize with blood meal (nitrogen) and fish emulsion. A great variety for Zone 5 is Little Marvel Pea. Watch video.