Build it up underneath the new countertop, with a mitered edge added to the countertop to make it look thicker and cover the plywood. It’s more expensive, though.

To add to Hillside House's suggestion, make sure that the wood you build up with matches the wood of the cabinets. Get someone good to do it, not just some random carpenter.

You did not mention whether you’ve checked the leveling legs under the range to see if they can be lowered.

Also you don’t want the range completely flush with the counters. That would be putting the flames on the same plane as an adjacent combustible surface. The rangetop should sit slightly proud of the adjacent counters, by about 1/4”.

Make sure your cabinet boxes can handle the weight of stone.

Investigate 'drop in ranges' as another option.

Thanks for the great suggestions! I also considered a cooktop as an option, but am not sure I can find an oven that will fit below, as in picture below. I believe this might be from Ikea, but could not find it on their website.

A drop in range includes the cooktop. It's all together.

Absolutely agree with Green Design. Get new cabinets build up the toekick area and then do your new countertop. If that isnt in your budget skip the stone, which wont look right with those cabinets anyway, and have it custom built thicker. Also make sure you either put the new floor under your dishwasher or you build the floor beneath it up to the same height before adding any countertop. Otherwise if you ever need to replace your dishwasher you can not. That is why a good flooring company always advises against flooring in old cabinets and appliances. Hind sight is 20/20. But you still have time to do this correctly not just a cosmetic mess.

And one further note, if you do a drop in cook top with a built in oven youll need cabinet to hold the oven and it wont match your cabinets. Same thing with a drop in range. And both are very expensive units and need custom work on the counter top.

One other option would be to build up on top of the existing cabinets, install the counter top and then cover the edge of the build up with molding . Flat thin stock, cove mold, shoe mold, etc.

From the photo, it appears that the cabinet face frame is oak and the drawer front is maple, I would use oak molding unless you are planning to paint. In that case, any species molding will work.

Cadyren... Old car with new paint job and nifty new rims is still an old car. So invest in the functional part of your kitch first then add the glitz and glamour. But seems people worry more about making things look good. Bit shsllowshallow. Do it right the first time even if it takes longer.

zellenpat your statement is true, however sometimes old things are better than new. It's all about your perspective & what you are wanting to do,

zellenpat in 2015 I inherited my mom's blue '91 Toyota Camry wagon which had 49,000 miles on it. It's got great visibility, gas mileage and it's comfortable. I've got to repaint it and replace the hubcaps, but I'll be driving it for years to come.