Day length is no problem. Orbital period is.
Day length mainly depends on how quickly a planet rotates around its own axis, modified slightly by its orbital period. There is nothing preventing a planet far from its sun to rotate at this speed. (The opposite is not true; a planet very close to its sun is likely to be tidally locked or in spin-orbit resonance).
Having the same year length when much farther out is quite a lot more difficult. As a general rule for stars of masses near that of the sun, the luminosity of a star is proportional to its mass to the fourth power, meaning that a planet's distance from its star to achieve the same amount of heat would be proportional to the square of the mass. For stars between 2 and twenty solar masses, luminosity is proportional to the mass to the power of 3.5; not that different. For stars above 55 solar masses, the relationship between mass and luminosity becomes linear, but such stars don't last very long because of strong solar winds and are unlikely to develop planets with life.
In return, the distance the planet needs to be from its sun to have the same orbital period (year) is proportional to the cube root of the star's mass. As a star grows bigger, planets with the same orbital period will be increasingly roasted by heat and radiation.
To achieve a similar year at a far greater distance (meaning a far heavier sun), you would need a stellar object with very little radiation compared to its mass. A possible solution would be a sun in close orbit around an even more masssive black hole, with your planet orbiting far from this pair.
Say that this star has twenty times the mass of our sun. It would have roughly 50,000 times the luminosity of our sun, so your planet would have to be roughly 225 times the distance of Earth from the sun to receive the same amount of sunlight. The mass of the black hole would hence have to be 11.4 million solar masses for the planet to have the same orbital period. This is a supermassive black hole, about three times more massive than the one at the center of our galaxy (but smaller than some in other galaxies).
Say that the star instead is only 5 solar masses, with a luminosity ca. 400 times that of our sun. The orbital distance of your planet would then have to be 20 times that of Earth's to receive the same heat; about the same as Uranus' orbit. The mass of the black hole would then 'only' have to be 8,000 solar masses; much more manageable. Whether black holes of this mass exist; between supermassive and stellar black holes; is unknown.