I'm not an astrophysicist or anything, so input from those with more knowledge on the subject is welcome, but I think if you started with a hotter, much more dense sun and put your planet's orbit further away to maintain the Earth-like atmosphere, the sun would be both objectively (in absolute measurements) and subjectively (as perceived from the planet) smaller, so there'd be less to eclipse. For good measure, nudged the moon a bit closer to the planet, and planetwide total eclipses should be possible. The trick is to maintain the balance of heat and mass of the sun relative to the planet's distance and orbital speed, so it maintains a stable orbit and doesn't spiral into the sun or reach escape velocity.
This may affect the length of the year (and/or day), but you can always fudge your calendar as you'd like, since they're arbitrary human measurements anyways. If the moon's orbit is synced with the planet's orbit around the sun, so the moon crosses between the planet and sun at exactly the same time every year, you'll have a once-a-year total eclipse. You could have your moon on a slightly off-plane orbit, and you might get one or three partial eclipses a year as it partially obscures the sun, then that one time of the year where it's in-plane with the sun and planet, causing your total eclipse.
Space.com has a great write-up on how eclipses occur -- even though the sun is larger than the moon, it's also much further away. Right now, the sun is about 400x away from us as the moon, and is about 400x larger than the moon, so we only get the eclipses when everything lines up just right. If the sun were further away or smaller, or the moon were larger or closer, or any combination of the above, planetwide eclipses could be entirely possible. You just have to mind the other astrophysical mechanics (mass, density, gravity, velocity, and so on) to make sure you don't have one of your celestial bodies spiraling toward or away from the other.
Fun fact: our moon is actually moving further away from the Earth by about 1.6 inches a year. In several thousand years, total solar eclipses might not be a thing any more!