Asparagus is a vegetable that thrives almost anywhere in Canada. Grow asparagus in well-drained soil with a neutral pH. (Add lime to the soil if it is acidic). Asparagus is usually planted in trenches from plants called crowns. Allow asparagus to grow without harvesting the year it is planted. In the second year, harvest spears that are 0.5 in. in diameter, but only for two weeks. In subsequent years, harvest for five to eight weeks, then allow the shoots to develop into ferny growth to build up the roots for the following year's crop.